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composition is continuous #1388

Merged
merged 4 commits into from
Nov 15, 2024
Merged

composition is continuous #1388

merged 4 commits into from
Nov 15, 2024

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zstone1
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@zstone1 zstone1 commented Nov 10, 2024

The last of the foundational bits for homotopy. The idea is simply that for nice spaces (E.G. locally compact) in the compact-open topology, composition itself is continuous. A couple small notes

  • Apparently the condition of local compactness of X is unnecessary (munrkes $46, ex. 7). But the proof here is much easier, and it shouldn't matter too much for us in the near future.
  • The regular_space condition is redundant due to locally_compact_completely_regular + completely_regular_regular. But those proofs sit in normed_type.v and need to be moved to separation_axioms.v before they can be used. Can be cleaned up later (or as a prerequisite if you think that's more important)
Checklist
  • added corresponding entries in CHANGELOG_UNRELEASED.md
  • added corresponding documentation in the headers

Reference: How to document

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@affeldt-aist
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continuous_curry_joint_cvg: why not simply continuous_curry_cvg?

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zstone1 commented Nov 13, 2024

Rename done. I'll merge once the master build is fixed.

@zstone1 zstone1 merged commit 91cd238 into math-comp:master Nov 15, 2024
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