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doc(topology/uniform_space/cauchy): fix typo (#12453)
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mcdoll committed Mar 5, 2022
1 parent bda091d commit 2840532
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2 changes: 1 addition & 1 deletion src/topology/uniform_space/cauchy.lean
Expand Up @@ -470,7 +470,7 @@ let ⟨t', ht', hct', htt'⟩ := mem_uniformity_is_closed ht, ⟨c, hcf, hc⟩ :
... ⊆ _ : Union₂_subset $ assume i hi, subset.trans (assume x, @htt' (x, i))
(subset_bUnion_of_mem hi)⟩

/-- The image of a totally bounded set under a unifromly continuous map is totally bounded. -/
/-- The image of a totally bounded set under a uniformly continuous map is totally bounded. -/
lemma totally_bounded.image [uniform_space β] {f : α → β} {s : set α}
(hs : totally_bounded s) (hf : uniform_continuous f) : totally_bounded (f '' s) :=
assume t ht,
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