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[Merged by Bors] - feat(continuous_function/compact): lemmas characterising norm and dist #7054

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Transport lemmas charactering the norm and distance on bounded continuous functions, to continuous maps with compact domain.


Splitting off a piece of #6497 for easier review.

Comment on lines 80 to 81
lemma dist_le_of_nonempty [nonempty α] :
dist f g ≤ C ↔ ∀ x, dist (f x) (g x) ≤ C :=
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This name seems odd - the statement is essentially the same as dist_lt_iff_of_nonempty, but dist_le_of_nonempty does not have iff in its name.

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I had just been following the names used in bounded_continuous_function. I've added an extra _iff in both places.

This does leave a discrepancy still: perhaps dist_le itself should be renamed to dist_le_iff? (In both bounded_continuous_function and continuous_map.)

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Thanks 🎉

bors merge

@github-actions github-actions bot added ready-to-merge All that is left is for bors to build and merge this PR. (Remember you need to say `bors r+`.) and removed awaiting-review The author would like community review of the PR labels Apr 7, 2021
bors bot pushed a commit that referenced this pull request Apr 7, 2021
#7054)

Transport lemmas charactering the norm and distance on bounded continuous functions, to continuous maps with compact domain.



Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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bors bot commented Apr 7, 2021

Pull request successfully merged into master.

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@bors bors bot changed the title feat(continuous_function/compact): lemmas characterising norm and dist [Merged by Bors] - feat(continuous_function/compact): lemmas characterising norm and dist Apr 7, 2021
@bors bors bot closed this Apr 7, 2021
@bors bors bot deleted the continuous_fn_compact_lemmas branch April 7, 2021 19:05
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3 participants