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Theorems · Theorem · general topology

IsUniformInducing.completeSpace

∀ {α : Type u} {β : Type v} [inst : UniformSpace α] [inst_1 : UniformSpace β] {f : α → β},
  IsUniformInducing f → IsComplete (Set.range f) → CompleteSpace α

Alias of the reverse direction of completeSpace_iff_isComplete_range.

Defined in
Mathlib.Topology.UniformSpace.UniformEmbedding
Cited by
1 results in Mathlib
Foundations
Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceUniformSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

TopologicalSpace.Compacts.completeSpace_iff · cited by 0Compacts.completeSpace_iffSet.range · cited by 4705Set.rangeCompleteSpace · cited by 2532CompleteSpaceUniformSpace · cited by 2040UniformSpaceIsUniformInducing · cited by 128IsUniformInducingIsComplete · cited by 68IsCompletecompleteSpace_iff_isComplete_range · cited by 11completeSpace_iff_isCompl…IsUniformInducing.completeSpa…CITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.