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subtypes and continuous functions

Open zstone1 opened this issue 1 year ago • 0 comments

Two related things. Now that pointed is gone from topology, we can canonically add topology/uniform/pseudometric on set_val. This now just a few easy instances.

Then we define a mixin for continuous functions. We build two structures from this. One is just Continuous for use with subtypes, and ContinuousFun for mixing with the Fun hierarchy using subspaces. And a bunch of lemmas for converting between them. Then we endow the set of continuous functions with various topologies in the ArrowAsT modules in function_spaces.v. In general I'd like to say "if arrow has a topology, then continuousType` inherits it, but I don't know how to say that in general, so it's fine to just manually do the instances in those modules.

Checklist
  • [ ] added corresponding entries in CHANGELOG_UNRELEASED.md
  • [ ] added corresponding documentation in the headers

Reference: How to document

Reminder to reviewers

zstone1 avatar Oct 06 '24 00:10 zstone1