[Merged by Bors] - feat: Topological properties of order-connected sets in ℝⁿ#10565
[Merged by Bors] - feat: Topological properties of order-connected sets in ℝⁿ#10565YaelDillies wants to merge 4 commits intomasterfrom
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Ruben-VandeVelde
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Seems pretty straightforward, modulo the removal of Topology.Order.Bounded
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Ruben-VandeVelde
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maintainer merge
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🚀 Pull request has been placed on the maintainer queue by Ruben-VandeVelde. |
fpvandoorn
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One more comment. Feel free to merge even if you disagree.
bors d+
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✌️ YaelDillies can now approve this pull request. To approve and merge a pull request, simply reply with |
| Is there a way to generalise `IsClosed.upperClosure_pi`/`IsClosed.lowerClosure_pi` so that they also | ||
| apply to `ℝ`, `ℝ × ℝ`, `EuclideanSpace ι ℝ`? `_pi` has been appended to their names to disambiguate | ||
| from the other possible lemmas, but we will want there to be a single set of lemmas for all | ||
| situations. |
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This comment shouldn't hold up this PR, but the relevant lemmas could just take a homeomorphism with a pi-type as an explicit argument. It's not a pretty solution, but I think it would work, and I believe we already have the necessary homeomorphisms available.
(On second thought, would it need to be an order isomorphism too? That probably rules out this idea as being useful)
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Yeah, it would also need to be an order isomorphism. That's the crux. We need a way to say "Order on this type is given by those coordinates", which sounds a lot like the Inducing/Embedding business in the topology part of the library.
Food for thought, I guess
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Partially forward-port leanprover-community/mathlib3#16976
Real.toNNReal_abs#11606