metric structure

[affeldt-aist]

Motivation for this change

@zstone1

Checklist

• [x] added corresponding entries in CHANGELOG_UNRELEASED.md

• [x] added corresponding documentation in the headers

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[affeldt-aist]

@zstone1 could this be the first step towards addressing issue #1437 ? This PR introduces a definition of metric space, move the lemma cvg_nbhsP from realfun.v to the directory topology_theory, incidentally together with at_left/at_right, which are now easier to move that normedtype.v has been split and reordered.

I propose to generalize a few more lemmas in the same manner, eventually moving a few things from normedtype_theory to topology_theory, so that we can arrive at a minimal PR introducing the metric structure without much disturbance for users. A complete generalization work can be carried incrementally. I am afraid that doing all the generalizations as a condition for merging will create a monster PR.

[zstone1]

Makes sense to add this. I'll note that there are a handful of places (itll take me a minute to find them all) where we use pseudometric + hausdorff instead of this. Might be nice for a followup PR to add a factory for hausdorff + pseudometric => metric too, and upgrade those places.

[affeldt-aist]

Many thanks for the comments, I should be able to address them later this week.