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Countable products of metrcs is metrizable

Open zstone1 opened this issue 3 years ago • 0 comments

Motivation for this change

Finally, we prove that countable products of metrics are metrizable! In particularly, the cantor set is metrizable. I have

  • A definition for countable_uniformity. Several lemmas use it, so it made sense to factor into a nicer definition. Note that this property is equivalent to metrizability, so it has little purpose outside of this family of proofs.
  • The main proof is that countable products preserve countable_uniformity. The definition of sup entourages is kinda annoying, so the proof is on the large side. It's not a blocker, just an inconvenience.
  • A bunch of definitions to build mixins and types.
Things done/to do
  • [x] added corresponding entries in CHANGELOG_UNRELEASED.md (do not edit former entries, only append new ones, be careful: merge and rebase have a tendency to mess up CHANGELOG_UNRELEASED.md)
  • [x] added corresponding documentation in the headers
Automatic note to reviewers

Read this Checklist and put a milestone if possible.

zstone1 avatar Oct 07 '22 02:10 zstone1