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[Merged by Bors] - feat: add Normed instances for SeparationQuotient#17452

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eric-wieser wants to merge 5 commits intomasterfrom
eric-wieser/SeparationQuotient-normed
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[Merged by Bors] - feat: add Normed instances for SeparationQuotient#17452
eric-wieser wants to merge 5 commits intomasterfrom
eric-wieser/SeparationQuotient-normed

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@eric-wieser eric-wieser commented Oct 5, 2024

We already have the corresponding metric spaces structures in MetricSpace.Basic.

This adds Algebra, NormOneClass, Normed(Add)CommGroup, (Nonunital)Normed(Comm)Ring, NormedSpace, and NormedAlgebra instances.

The slightly heavy imports here can be blamed on Topology.Algebra.SeparationQuotient importing LinearAlgebra.Basis.VectorSpace for the final 50-100 lines of the file. Moving this to a new file would cut the chain, as would generalizing it to work in free modules (continuing from #17560), assuming it actually holds there.


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@eric-wieser eric-wieser added the t-analysis Analysis (normed *, calculus) label Oct 5, 2024
@eric-wieser eric-wieser requested a review from urkud October 5, 2024 16:52
@github-actions github-actions bot added the large-import Automatically added label for PRs with a significant increase in transitive imports label Oct 5, 2024
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PR summary ed24d36c19

Import changes exceeding 2%

% File
+3.51% Mathlib.Analysis.Normed.Field.Lemmas
+12.62% Mathlib.Analysis.Normed.Group.Uniform
+3.24% Mathlib.Analysis.Normed.Module.Basic
+13.09% Mathlib.Topology.MetricSpace.Algebra

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.Topology.MetricSpace.Algebra 1016 1149 +133 (+13.09%)
Mathlib.Analysis.Normed.Group.Uniform 1030 1160 +130 (+12.62%)
Mathlib.Analysis.Normed.Field.Lemmas 1196 1238 +42 (+3.51%)
Mathlib.Analysis.Normed.Module.Basic 1202 1241 +39 (+3.24%)
Import changes for all files
Files Import difference
650 files Mathlib.MeasureTheory.Integral.VitaliCaratheodory Mathlib.Analysis.MeanInequalitiesPow Mathlib.Analysis.CStarAlgebra.GelfandDuality Mathlib.Probability.Process.HittingTime Mathlib.NumberTheory.Liouville.LiouvilleWith Mathlib.Analysis.InnerProductSpace.Spectrum Mathlib.Analysis.InnerProductSpace.Symmetric Mathlib.Analysis.InnerProductSpace.OfNorm Mathlib.NumberTheory.Cyclotomic.Rat Mathlib.Analysis.Calculus.Deriv.Pi Mathlib.Analysis.Calculus.Deriv.Inv Mathlib.Probability.BorelCantelli Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv Mathlib.Geometry.Manifold.ContMDiff.Atlas Mathlib.NumberTheory.LSeries.HurwitzZetaValues Mathlib.Analysis.SpecialFunctions.Gamma.Basic Mathlib.Geometry.Manifold.VectorBundle.Pullback Mathlib.Analysis.NormedSpace.HahnBanach.SeparatingDual Mathlib.Analysis.Convex.AmpleSet Mathlib.Probability.Variance Mathlib.Analysis.NormedSpace.OperatorNorm.Basic Mathlib.Analysis.Complex.Angle Mathlib.LinearAlgebra.Matrix.PosDef Mathlib.Analysis.SpecialFunctions.Integrals Mathlib.NumberTheory.Harmonic.ZetaAsymp Mathlib.Dynamics.Ergodic.AddCircle Mathlib.Analysis.Calculus.BumpFunction.Convolution Mathlib.Analysis.Fourier.PoissonSummation Mathlib.Analysis.InnerProductSpace.Rayleigh Mathlib.Analysis.Normed.Module.Dual Mathlib.NumberTheory.Cyclotomic.Discriminant Mathlib.Geometry.Manifold.VectorBundle.Basic Mathlib.Analysis.Calculus.Deriv.Abs Mathlib.Analysis.CStarAlgebra.Multiplier Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds Mathlib.Analysis.Calculus.Deriv.Star Mathlib.MeasureTheory.Measure.FiniteMeasure Mathlib.Tactic.FunProp.ContDiff Mathlib.MeasureTheory.Integral.IntervalAverage Mathlib.Analysis.Distribution.FourierSchwartz Mathlib.Analysis.Normed.Lp.PiLp Mathlib.Analysis.Calculus.ParametricIntervalIntegral Mathlib.MeasureTheory.Measure.ProbabilityMeasure Mathlib.Geometry.Manifold.VectorBundle.Tangent Mathlib.Analysis.Calculus.Deriv.Add Mathlib.MeasureTheory.Function.UnifTight 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Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform Mathlib.MeasureTheory.Function.LpSpace.DomAct.Continuous Mathlib.Geometry.Euclidean.PerpBisector Mathlib.MeasureTheory.Group.Integral Mathlib.Analysis.Normed.Affine.ContinuousAffineMap Mathlib.MeasureTheory.Measure.Haar.Disintegration Mathlib.Analysis.Distribution.SchwartzSpace Mathlib.Probability.Integration Mathlib.NumberTheory.Bertrand Mathlib.Analysis.Calculus.LocalExtr.Rolle Mathlib.Geometry.Manifold.Metrizable Mathlib.Analysis.BoxIntegral.DivergenceTheorem Mathlib.NumberTheory.LSeries.Convolution Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral Mathlib.Analysis.Calculus.LocalExtr.LineDeriv Mathlib.MeasureTheory.Measure.WithDensityVectorMeasure Mathlib.Analysis.SpecialFunctions.Pow.Integral Mathlib.Geometry.Manifold.WhitneyEmbedding Mathlib.Topology.ContinuousMap.Ideals Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic Mathlib.Analysis.SpecialFunctions.Trigonometric.Series Mathlib.Probability.Kernel.Integral Mathlib.MeasureTheory.Integral.Average Mathlib.Probability.Kernel.Disintegration.Unique Mathlib.Analysis.Convex.PartitionOfUnity Mathlib.LinearAlgebra.Matrix.HermitianFunctionalCalculus Mathlib.Probability.Independence.Conditional Mathlib.Analysis.SpecialFunctions.Sqrt Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic Mathlib.MeasureTheory.Function.ConditionalExpectation.Real Mathlib.RingTheory.Perfection Mathlib.Data.Real.Pi.Wallis Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt Mathlib.Probability.Process.PartitionFiltration Mathlib.Probability.Notation Mathlib.NumberTheory.LSeries.AbstractFuncEq Mathlib.Probability.CDF Mathlib.Analysis.Normed.Module.Completion Mathlib.Topology.MetricSpace.Ultra.ContinuousMaps Mathlib.MeasureTheory.Measure.Haar.OfBasis Mathlib.Data.Complex.ExponentialBounds Mathlib.Analysis.InnerProductSpace.TwoDim Mathlib.Probability.Martingale.Centering Mathlib.MeasureTheory.Measure.Haar.Quotient Mathlib.Geometry.Manifold.Instances.Sphere Mathlib.Geometry.Manifold.VectorBundle.SmoothSection Mathlib.Geometry.Manifold.ContMDiff.Product Mathlib.Analysis.InnerProductSpace.LaxMilgram Mathlib.Analysis.Normed.Algebra.UnitizationL1
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4 files Mathlib.RingTheory.WittVector.Compare Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas Mathlib.NumberTheory.SumTwoSquares
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Mathlib.Topology.Category.Profinite.Nobeling 3
70 files Mathlib.Combinatorics.SimpleGraph.Triangle.Removal Mathlib.Dynamics.TopologicalEntropy.NetEntropy Mathlib.NumberTheory.MulChar.Lemmas Mathlib.Analysis.SpecialFunctions.Pow.Complex Mathlib.MeasureTheory.Function.SpecialFunctions.Basic Mathlib.Analysis.SpecialFunctions.CompareExp Mathlib.Combinatorics.Additive.Corner.Roth Mathlib.MeasureTheory.Function.LpSeminorm.Basic Mathlib.Analysis.SpecialFunctions.Complex.Log Mathlib.Topology.ContinuousMap.Polynomial Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital Mathlib.Analysis.Complex.HalfPlane Mathlib.Analysis.Complex.UnitDisc.Basic Mathlib.Analysis.SpecialFunctions.Exp Mathlib.Analysis.Normed.Algebra.Norm Mathlib.Computability.AkraBazzi.GrowsPolynomially Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan Mathlib.Analysis.Complex.Circle Mathlib.Analysis.SpecialFunctions.PolynomialExp Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unitary Mathlib.NumberTheory.SumPrimeReciprocals Mathlib.MeasureTheory.Function.LpSeminorm.Trim Mathlib.Analysis.PSeries Mathlib.Analysis.Complex.Basic Mathlib.NumberTheory.EulerProduct.Basic Mathlib.Analysis.SpecialFunctions.Pow.Continuity Mathlib.Analysis.SpecialFunctions.Log.ENNRealLogExp Mathlib.NumberTheory.ClassNumber.AdmissibleCardPowDegree Mathlib.Combinatorics.SimpleGraph.Regularity.Increment Mathlib.Analysis.SpecificLimits.FloorPow Mathlib.Analysis.Normed.Ring.SeminormFromConst Mathlib.Analysis.Complex.IsIntegral Mathlib.Analysis.SpecialFunctions.Log.Base Mathlib.Analysis.Convex.SpecificFunctions.Pow Mathlib.Analysis.Normed.Ring.Seminorm Mathlib.MeasureTheory.Function.LpSeminorm.ChebyshevMarkov Mathlib.MeasureTheory.Function.SpecialFunctions.Arctan Mathlib.Analysis.Complex.ReImTopology Mathlib.Analysis.SpecialFunctions.Complex.Arg Mathlib.NumberTheory.Ostrowski Mathlib.MeasureTheory.Measure.Doubling Mathlib.Analysis.Normed.Ring.SeminormFromBounded Mathlib.Analysis.Complex.Asymptotics Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex Mathlib.MeasureTheory.Constructions.BorelSpace.Complex Mathlib.RingTheory.RootsOfUnity.Complex Mathlib.Analysis.SpecialFunctions.Log.Monotone Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics Mathlib.Topology.Algebra.PontryaginDual Mathlib.Topology.MetricSpace.Holder Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk Mathlib.Analysis.SpecialFunctions.Log.Basic Mathlib.NumberTheory.VonMangoldt Mathlib.Analysis.SpecialFunctions.Pow.Real Mathlib.Analysis.SpecialFunctions.Trigonometric.Angle Mathlib.Analysis.Normed.Ring.IsPowMulFaithful Mathlib.NumberTheory.Padics.Hensel Mathlib.Algebra.Order.CompleteField Mathlib.Combinatorics.SimpleGraph.Regularity.Bound Mathlib.Dynamics.TopologicalEntropy.CoverEntropy Mathlib.Analysis.SpecialFunctions.Complex.Circle Mathlib.Combinatorics.SimpleGraph.Regularity.Lemma Mathlib.NumberTheory.Padics.ProperSpace Mathlib.Analysis.SpecialFunctions.Pow.NNReal Mathlib.Analysis.Convex.SpecificFunctions.Basic Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic Mathlib.MeasureTheory.Measure.Complex Mathlib.Analysis.Complex.AbelLimit Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog
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3 files Mathlib.NumberTheory.Padics.PadicIntegers Mathlib.Topology.Algebra.Polynomial Mathlib.NumberTheory.Padics.RingHoms
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12 files Mathlib.Condensed.Limits Mathlib.Condensed.Light.Explicit Mathlib.Condensed.Explicit Mathlib.Condensed.Module Mathlib.Condensed.Light.CartesianClosed Mathlib.Condensed.Solid Mathlib.Condensed.Discrete.Module Mathlib.Condensed.Light.Epi Mathlib.Condensed.Light.Limits Mathlib.Condensed.CartesianClosed Mathlib.Condensed.Light.Module Mathlib.Condensed.Epi
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Mathlib.Analysis.LocallyConvex.ContinuousOfBounded 24
9 files Mathlib.Analysis.Convex.Body Mathlib.Analysis.NormedSpace.RieszLemma Mathlib.Analysis.Normed.Group.Tannery Mathlib.Topology.Algebra.Module.Alternating.Topology Mathlib.Topology.ContinuousMap.Units Mathlib.Analysis.RCLike.Basic Mathlib.Analysis.CStarAlgebra.Basic Mathlib.Dynamics.BirkhoffSum.NormedSpace Mathlib.Analysis.SpecificLimits.RCLike
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8 files Mathlib.Topology.Algebra.Module.UniformConvergence Mathlib.Analysis.LocallyConvex.Bounded Mathlib.Analysis.NormedSpace.Extr Mathlib.Topology.Algebra.Module.StrongTopology Mathlib.Topology.Algebra.Module.Multilinear.Bounded Mathlib.Analysis.Normed.Module.Ray Mathlib.Topology.Algebra.Module.Multilinear.Topology Mathlib.Analysis.Normed.Operator.Compact
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8 files Mathlib.Analysis.Seminorm Mathlib.Analysis.LocallyConvex.Basic Mathlib.Analysis.Convex.EGauge Mathlib.Analysis.Normed.Ring.Units Mathlib.Analysis.SpecificLimits.Normed Mathlib.Analysis.Normed.Group.ControlledClosure Mathlib.Analysis.LocallyConvex.BalancedCoreHull Mathlib.Topology.Algebra.Module.Cardinality
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60 files Mathlib.Topology.Category.Stonean.Adjunctions Mathlib.Topology.Category.LightProfinite.EffectiveEpi Mathlib.Topology.Category.Stonean.EffectiveEpi Mathlib.Probability.Distributions.Geometric Mathlib.Topology.Category.CompHaus.EffectiveEpi Mathlib.Topology.Category.Profinite.CofilteredLimit Mathlib.Condensed.TopComparison Mathlib.Condensed.Discrete.Basic Mathlib.Topology.Category.LightProfinite.Extend Mathlib.Topology.Category.Profinite.EffectiveEpi Mathlib.Analysis.Normed.Affine.Isometry Mathlib.Topology.Category.Profinite.AsLimit Mathlib.Topology.CompletelyRegular Mathlib.Condensed.Basic Mathlib.Condensed.Light.TopComparison Mathlib.Condensed.Light.TopCatAdjunction Mathlib.Condensed.Discrete.LocallyConstant Mathlib.Analysis.Normed.Module.Span Mathlib.Analysis.Normed.Affine.MazurUlam Mathlib.Analysis.Normed.Group.SemiNormedGrp.Kernels Mathlib.Topology.Category.LightProfinite.AsLimit Mathlib.Topology.Category.LightProfinite.Limits Mathlib.Analysis.Normed.Group.Quotient Mathlib.Topology.Category.CompHaus.Basic Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic Mathlib.Topology.Category.CompHaus.Projective Mathlib.Analysis.NormedSpace.ConformalLinearMap Mathlib.Topology.Category.Profinite.Projective Mathlib.Topology.PartitionOfUnity Mathlib.Topology.Category.Profinite.Basic Mathlib.MeasureTheory.Integral.LebesgueNormedSpace Mathlib.Topology.Category.CompHaus.Limits Mathlib.Condensed.TopCatAdjunction Mathlib.Probability.Kernel.Disintegration.MeasurableStieltjes Mathlib.Topology.UrysohnsLemma Mathlib.Topology.Category.CompactlyGenerated Mathlib.Analysis.Normed.Group.AddCircle Mathlib.Topology.Category.Compactum Mathlib.Analysis.NormedSpace.HomeomorphBall Mathlib.Topology.Category.Profinite.Extend Mathlib.Topology.Compactness.CompactlyGeneratedSpace Mathlib.Topology.Category.Stonean.Basic Mathlib.MeasureTheory.Function.Egorov Mathlib.Topology.Category.LightProfinite.Basic Mathlib.Topology.Category.LightProfinite.Sequence Mathlib.Condensed.Light.Basic Mathlib.Dynamics.Ergodic.Function Mathlib.Topology.Category.Locale Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic Mathlib.Order.Category.Frm Mathlib.Condensed.Light.Functors Mathlib.MeasureTheory.Function.AEEqFun Mathlib.Condensed.Functors Mathlib.Condensed.Equivalence Mathlib.Topology.Category.Profinite.Product Mathlib.Topology.Category.Profinite.Limits Mathlib.MeasureTheory.Measure.EverywherePos Mathlib.Topology.Order.Category.FrameAdjunction Mathlib.Analysis.NormedSpace.Pointwise Mathlib.Topology.Category.Stonean.Limits
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6 files Mathlib.Analysis.Normed.Order.UpperLower Mathlib.Analysis.Normed.Group.Completeness Mathlib.Analysis.Normed.Field.ProperSpace Mathlib.Analysis.Normed.Affine.AddTorsor Mathlib.Analysis.Normed.Group.Pointwise Mathlib.Analysis.NormedSpace.Real
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Mathlib.Analysis.SpecialFunctions.Polynomials 36
8 files Mathlib.Analysis.Asymptotics.SpecificAsymptotics Mathlib.Analysis.Asymptotics.AsymptoticEquivalent Mathlib.Topology.Germ Mathlib.Analysis.NormedSpace.ENorm Mathlib.Analysis.Asymptotics.Theta Mathlib.Analysis.Normed.Module.Basic Mathlib.Analysis.NormedSpace.BallAction Mathlib.Analysis.NormedSpace.SphereNormEquiv
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Mathlib.Analysis.Normed.Operator.ContinuousLinearMap 40
Mathlib.Order.Filter.ZeroAndBoundedAtFilter 41
10 files Mathlib.Topology.Bornology.BoundedOperation Mathlib.NumberTheory.Padics.PadicNumbers Mathlib.Analysis.Normed.Field.UnitBall Mathlib.NumberTheory.Harmonic.Int Mathlib.Analysis.Normed.Order.Basic Mathlib.Analysis.NormedSpace.Int Mathlib.Analysis.Asymptotics.SuperpolynomialDecay Mathlib.Analysis.Normed.Field.Lemmas Mathlib.Analysis.Normed.Field.InfiniteSum Mathlib.Analysis.Asymptotics.Asymptotics
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Mathlib.Analysis.Normed.Operator.LinearIsometry 49
Mathlib.Analysis.Normed.MulAction Mathlib.Analysis.Normed.Ring.Ultra 66
Mathlib.Analysis.Normed.Group.Ultra 80
Mathlib.Analysis.NormedSpace.FunctionSeries 91
7 files Mathlib.Analysis.Normed.Group.HomCompletion Mathlib.Analysis.Normed.Group.Completion Mathlib.Analysis.Normed.Group.InfiniteSum Mathlib.Analysis.Normed.Group.Lemmas Mathlib.Analysis.Normed.Group.SemiNormedGrp.Completion Mathlib.Analysis.Normed.Order.Lattice Mathlib.Topology.MetricSpace.Completion
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Mathlib.Analysis.Normed.Group.SemiNormedGrp 123
Mathlib.Analysis.Normed.Group.Hom 128
Mathlib.Analysis.Normed.Group.Uniform Mathlib.Analysis.Normed.Group.BallSphere 130
Mathlib.Topology.MetricSpace.Algebra 133

Declarations diff

+ Inseparable.nnnorm_eq_nnnorm'
+ Inseparable.norm_eq_norm'
+ SeparationQuotient.instNormedAlgebra
+ SeparationQuotient.instNormedSpace
+ instAlgebra
+ instMulNorm
+ instance (priority := 100) NonUnitalSeminormedRing.toContinuousMul [NonUnitalSeminormedRing α] :
+ instance (priority := 100) NonUnitalSeminormedRing.toTopologicalRing [NonUnitalSeminormedRing α] :
+ instance : NormedCommGroup (SeparationQuotient E)
+ instance [NonUnitalSeminormedCommRing α] : NonUnitalNormedCommRing (SeparationQuotient α)
+ instance [NonUnitalSeminormedRing α] : NonUnitalNormedRing (SeparationQuotient α)
+ instance [SeminormedAddCommGroup α] [One α] [NormOneClass α] :
+ instance [SeminormedCommRing α] : NormedCommRing (SeparationQuotient α)
+ instance [SeminormedRing α] : NormedRing (SeparationQuotient α)
+ instance {α β : Type*}
+ mkRingHom
+ mk_algebraMap
+ nnnorm_mk'
+ norm_mk'
- instance (priority := 100) semi_normed_ring_top_monoid [NonUnitalSeminormedRing α] :
- instance (priority := 100) semi_normed_top_ring [NonUnitalSeminormedRing α] :

You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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Thanks!
It seems that the large import change only relies on the import of LinearAlgebra.Basis.VectorSpace in Topology.Algebra.SeparationQuotient, which is used only for that result, so if you want to change things a bit that would be easy to avoid (but I don't really care).

bors d+

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mathlib-bors bot commented Oct 8, 2024

✌️ eric-wieser can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@ghost ghost added the delegated This pull request has been delegated to the PR author (or occasionally another non-maintainer). label Oct 8, 2024
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It seems that the large import change only relies on the import of LinearAlgebra.Basis.VectorSpace in Topology.Algebra.SeparationQuotient, which is used only for that result, so if you want to change things a bit that would be easy to avoid (but I don't really care).

Thanks for spotting this; I'll leave a note in the PR description that someone who does care could follow up with this refactor.

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bors merge

@github-actions github-actions bot added the ready-to-merge This PR has been sent to bors. label Oct 8, 2024
mathlib-bors bot pushed a commit that referenced this pull request Oct 8, 2024
We already have the corresponding metric spaces structures in `MetricSpace.Basic`.

This adds `Algebra`, `NormOneClass`, `Normed(Add)CommGroup`, `(Nonunital)Normed(Comm)Ring`, `NormedSpace`, and `NormedAlgebra` instances.

The slightly heavy imports here can be blamed on `Topology.Algebra.SeparationQuotient` importing `LinearAlgebra.Basis.VectorSpace` for the final 50-100 lines of the file. Moving this to a new file would cut the chain, as would generalizing it to work in free modules (continuing from #17560), assuming it actually holds there.
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mathlib-bors bot commented Oct 8, 2024

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat: add Normed instances for SeparationQuotient [Merged by Bors] - feat: add Normed instances for SeparationQuotient Oct 8, 2024
@mathlib-bors mathlib-bors bot closed this Oct 8, 2024
@mathlib-bors mathlib-bors bot deleted the eric-wieser/SeparationQuotient-normed branch October 8, 2024 23:52
yoh-tanimoto added a commit that referenced this pull request Oct 9, 2024
mathlib-bors bot pushed a commit that referenced this pull request Nov 15, 2024
…nQuotient): add null subspaces (#16707)

Define the null submodule in an `InnerProductSpace` and the null subgroup in a `NormedAddCommGroup` and prove basic properties.

~~Define the null space in an `InnerProductSpace` without `definite` and add `InnerProduceSpace` structure to the quotient by the null space.~~ 

Motivation: This PR has evolved from a PR defining the `SeparationQuotient` for `InnerProductSpace`. That has been done in #17452 and now contains some other things.



Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Co-authored-by: Yoh Tanimoto <57562556+yoh-tanimoto@users.noreply.github.com>
TobiasLeichtfried pushed a commit that referenced this pull request Nov 21, 2024
…nQuotient): add null subspaces (#16707)

Define the null submodule in an `InnerProductSpace` and the null subgroup in a `NormedAddCommGroup` and prove basic properties.

~~Define the null space in an `InnerProductSpace` without `definite` and add `InnerProduceSpace` structure to the quotient by the null space.~~ 

Motivation: This PR has evolved from a PR defining the `SeparationQuotient` for `InnerProductSpace`. That has been done in #17452 and now contains some other things.



Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Co-authored-by: Yoh Tanimoto <57562556+yoh-tanimoto@users.noreply.github.com>
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delegated This pull request has been delegated to the PR author (or occasionally another non-maintainer). large-import Automatically added label for PRs with a significant increase in transitive imports ready-to-merge This PR has been sent to bors. t-analysis Analysis (normed *, calculus)

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