[Merged by Bors] - feat: general Ascoli theorem #6844
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| * In Bourbaki, the usual Arzela-Ascoli compactness theorem follows from a similar total boundedness | ||
| result. Here we go directly for the compactness result, which is the most useful in practice, but | ||
| this will be an easy addition/refactor if we ever need it. |
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Could you clarify what you mean by "this" here: I presume you mean establishing the intermediate total boundedness result a la Bourbaki?
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Don't you want me to change this before merging? I was planning to do it tomorrow morning. I can also change the wording later if you want.
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I decided I was splitting hairs and it wasn't worth delaying this PR any further.
Feel free to follow up with a doc string adjustment PR or not, according to your taste!
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Co-authored-by: Oliver Nash <github@olivernash.org>
…hlib4 into AD_ascoli_part1
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bors merge |
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Co-authored-by: @vbeffara (port to Lean4), @tb65536 (suggested to skip the totally bounded case and go straight to compactness using Tykhonov) This was discussed on Zulip [recently](https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/Arzela-Ascoli.20for.20uniform.20spaces) and [a while ago](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Montel's.20theorem).
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Louddy
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Co-authored-by: @vbeffara (port to Lean4), @tb65536 (suggested to skip the totally bounded case and go straight to compactness using Tykhonov) This was discussed on Zulip [recently](https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/Arzela-Ascoli.20for.20uniform.20spaces) and [a while ago](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Montel's.20theorem).
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Co-authored-by: @vbeffara (port to Lean4), @tb65536 (suggested to skip the totally bounded case and go straight to compactness using Tykhonov) This was discussed on Zulip [recently](https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/Arzela-Ascoli.20for.20uniform.20spaces) and [a while ago](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Montel's.20theorem).
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Co-authored-by: @vbeffara (port to Lean4), @tb65536 (suggested to skip the totally bounded case and go straight to compactness using Tykhonov) This was discussed on Zulip [recently](https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/Arzela-Ascoli.20for.20uniform.20spaces) and [a while ago](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Montel's.20theorem).
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Co-authored-by: @vbeffara (port to Lean4), @tb65536 (suggested to skip the totally bounded case and go straight to compactness using Tykhonov) This was discussed on Zulip [recently](https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/Arzela-Ascoli.20for.20uniform.20spaces) and [a while ago](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Montel's.20theorem).
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Co-authored-by: @vbeffara (port to Lean4), @tb65536 (suggested to skip the totally bounded case and go straight to compactness using Tykhonov)
This was discussed on Zulip recently and a while ago.