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[Merged by Bors] - feat(continuous_function/compact): lemmas characterising norm and dist #7054
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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
#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>
Pull request successfully merged into master. Build succeeded: |
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.