[Merged by Bors] - feat: Ico, Ioc, and Ioo are not closed or compact#20479
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eric-wieser wants to merge 9 commits intomasterfrom
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[Merged by Bors] - feat: Ico, Ioc, and Ioo are not closed or compact#20479eric-wieser wants to merge 9 commits intomasterfrom
Ico, Ioc, and Ioo are not closed or compact#20479eric-wieser wants to merge 9 commits intomasterfrom
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PR summary 40f4de7f20Import changes for modified filesNo significant changes to the import graph Import changes for all files
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Ico, Ioc, and Ioo are not compactIco, Ioc, and Ioo are not closed or compact
Ruben-VandeVelde
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Makes sense to me
maintainer merge
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🚀 Pull request has been placed on the maintainer queue by Ruben-VandeVelde. |
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bors r+ |
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Inspired by [this Zulip thread](https://leanprover.zulipchat.com/#narrow/channel/113489-new-members/topic/Proving.20compactness.20of.20.280.2Cr.5D.20from.20.5B0.2Cr.5D/near/491839141) which tried to prove a false result. Also includes 12 stupid lemmas about interval equalities to make `simp` slightly more helpful. I don't know if the topological results can be generalized further, but these lemmas at least work for `Real` as was needed on Zulip.
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Pull request successfully merged into master. Build succeeded: |
Ico, Ioc, and Ioo are not closed or compactIco, Ioc, and Ioo are not closed or compact
Julian
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* origin/master: (133 commits) chore(1000): remove nonexistent fields (#20493) chore(CategoryTheory/Adjunction.Basic, CategoryTheory/Equivalence): change definition of `Adjunction.comp` and `Equivalence.trans` (#20490) feat(Asymptotics): add `Asymptotics.*.*Prod` lemmas (#20458) feat: a conditional kernel is almost everywhere a probability measure (#20430) feat: if `f` is a measurable group hom, then every point has a neighborhood `s` such that `f '' s` is bounded (#20304) feat: `Ico`, `Ioc`, and `Ioo` are not closed or compact (#20479) chore: drop redundant hypothesis in `Module.Dual.eq_of_preReflection_mapsTo` (#20492) feat(FaaDiBruno): derive `DecidableEq` (#20482) chore(SetTheory/Ordinal/Basic): `{x // x < y}` → `Iio y` (#20413) chore: generalize `FormalMultilinearSeries.ofScalars_norm` to `Seminormed` (#20351) chore(MvPolynomial/Localization): golf using TensorProduct (#20309) chore(Combinatorics/Enumerative/Partition): auto-derive DecidableEq (#20277) chore(CategoryTheory): make relevant parameters explicit in `Arrow.homMk`. (#20259) feat: add `IsStarNormal (↑x⁻¹ : R)` instance for `x : Rˣ` (#20091) fix: Stop cancelling builds of master (#20435) chore: update Mathlib dependencies 2025-01-05 (#20485) feat(SetTheory/Cardinal/Arithmetic): miscellaneous cardinality lemmas (#18933) chore: bump toolchain to v4.16.0-rc1, and merge bump/v4.16.0 (#20464) chore: bot validates lean-toolchain on bump/v4.X.0 branches (#20478) feat: shorthand lemmas for the L1 norm (#20383) chore: remove unnecessary adaptation notes (#20467) chore(Algebra/Category/MonCat/Colimits): remove smallness condition (#20473) chore(SetTheory/Ordinal/Arithmetic): `IsLeftCancelAdd Ordinal` (#19888) feat(Algebra): more on `OrthogonalIdempotents` (#18195) feat(Radical): `(radical a).natDegree ≤ a.natDegree` (#20468) feat(Polynomial): `(a^n)' = 0` iff `a' = 0` when `n` doesn't divide the characteristic (#20190) feat(Algebra/Lie): add Lie's theorem (#13480) chore(RingTheory/Generators): make algebra instance a def (#14265) feat(Topology/Group): Lemmas about profinite group (#20282) feat: the empty set is a topological basis iff the space is empty (#20441) chore: make uniqueness of conditionally complete linearly ordered archimedean fields independent of the construction of `Real` (#20242) chore: `inherit_doc`s for notations (#20376) chore: split AEEqOfIntegral into two files, one for each integral type (#20405) chore: split Kernel/MeasurableIntegral (#20427) feat(MeasureTheory/Group/Measure): add ContinuousMulEquiv.isHaarMeasure_map (#20469) fix(Mathlib.Tactic.CC.Datatypes): `cc` raises panic (#20422) feat(Probability/Moments): add lemmas about moment generating functions (#19886) feat(Algebra/Order/AddGroupWithTop): lemmas about LinearOrderedAddCommGroupWithTop (#18954) chore: bump toolchain to v4.15.0 (#20461) chore: update Mathlib dependencies 2025-01-04 (#20463) fix: make `Prod` projection delaborators respond to options, add option to disable (#20455) chore(Algebra): Improve attribute generation (#20451) feat(Polynomial): `(C a * p).degree = p.degree` if `a * p.leadingCoeff ≠ 0` (#20446) feat: add `ENNReal.finStronglyMeasurable_of_measurable` (#20404) doc(Algebra/Lie/Weights/Basic): fix typo (#20450) chore(1000): remove `identifiers` (#20445) feat: add sumPiEquivProdPi and piUnique (#20195) feat: add fst_compProd_apply (#20429) chore: use unsigned measures for Lebesgue decomposition (#20400) feat: Two lemmas on divisibility and coprimality of `expand` (#20143) ...
Julian
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* origin/master: (189 commits) chore(Algebra): make more names consistent (#20449) feat: Polynomial FLT (#18882) feat: A disjoint union is finite iff all sets are finite, and all but finitely many are empty (#20457) fix: linkfix in 100.yaml (#20517) feat(1000): fill in more entries (#20470) feat(Combinatorics/SimpleGraph/Walk): add `penultimate` and `snd` (#16769) feat(ContinuousMultilinearMap): add lemmas about `.prod` (#20462) feat(RingTheory): classification of etale algebras over fields (#20324) fix: Allow multiple builds on staging branch (#20515) feat(CategoryTheory/Shift/Adjunction): properties of `Adjunction.CommShift` (#20337) chore(Data/Multiset/Basic): move the `sub`, `union`, `inter` sections lower (#19863) chore(Topology/UniformSpace/Completion): make coe' argument implicit (#20514) refactor(Algebra/Category/Grp/Colimits): change the construction of colimits in `AddCommGrp` (#20474) feat(Topology/Algebra/InfiniteSum/NatInt): Add pnat lems (#16544) chore(RingTheory/Finiteness): rename Module.Finite.out (#20506) refactor(CategoryTheory/Limits/Preserves/Ulift): simplify the proof that the universe lifting functor for types preserves all colimits (#20508) feat(CategoryTheory): products in the category of Ind-objects (#20507) chore: remove >9 month old deprecations (#20505) chore(FieldTheory/Galois): small cleanup (#20217) chore(LinearIndependent): generalize to semirings (#20480) chore(NumberTheory/NumberField/AdeleRing): refactor adele rings (#20500) chore: replace `aesop` with `simp` where possible (#20483) chore(1000): remove nonexistent fields (#20493) chore(CategoryTheory/Adjunction.Basic, CategoryTheory/Equivalence): change definition of `Adjunction.comp` and `Equivalence.trans` (#20490) feat(Asymptotics): add `Asymptotics.*.*Prod` lemmas (#20458) feat: a conditional kernel is almost everywhere a probability measure (#20430) feat: if `f` is a measurable group hom, then every point has a neighborhood `s` such that `f '' s` is bounded (#20304) feat: `Ico`, `Ioc`, and `Ioo` are not closed or compact (#20479) chore: drop redundant hypothesis in `Module.Dual.eq_of_preReflection_mapsTo` (#20492) feat(FaaDiBruno): derive `DecidableEq` (#20482) chore(SetTheory/Ordinal/Basic): `{x // x < y}` → `Iio y` (#20413) chore: generalize `FormalMultilinearSeries.ofScalars_norm` to `Seminormed` (#20351) chore(MvPolynomial/Localization): golf using TensorProduct (#20309) chore(Combinatorics/Enumerative/Partition): auto-derive DecidableEq (#20277) chore(CategoryTheory): make relevant parameters explicit in `Arrow.homMk`. (#20259) feat: add `IsStarNormal (↑x⁻¹ : R)` instance for `x : Rˣ` (#20091) fix: Stop cancelling builds of master (#20435) chore: update Mathlib dependencies 2025-01-05 (#20485) feat(SetTheory/Cardinal/Arithmetic): miscellaneous cardinality lemmas (#18933) chore: bump toolchain to v4.16.0-rc1, and merge bump/v4.16.0 (#20464) chore: bot validates lean-toolchain on bump/v4.X.0 branches (#20478) feat: shorthand lemmas for the L1 norm (#20383) chore: remove unnecessary adaptation notes (#20467) chore(Algebra/Category/MonCat/Colimits): remove smallness condition (#20473) chore(SetTheory/Ordinal/Arithmetic): `IsLeftCancelAdd Ordinal` (#19888) feat(Algebra): more on `OrthogonalIdempotents` (#18195) feat(Radical): `(radical a).natDegree ≤ a.natDegree` (#20468) feat(Polynomial): `(a^n)' = 0` iff `a' = 0` when `n` doesn't divide the characteristic (#20190) feat(Algebra/Lie): add Lie's theorem (#13480) chore(RingTheory/Generators): make algebra instance a def (#14265) ...
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Inspired by this Zulip thread which tried to prove a false result.
Also includes 12 stupid lemmas about interval equalities to make
simpslightly more helpful.I don't know if the topological results can be generalized further, but these lemmas at least work for
Realas was needed on Zulip.