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Theorems · Theorem · general topology

isUniformEmbedding_iff

∀ {α : Type ua} {β : Type ub} [inst : UniformSpace α] [inst_1 : UniformSpace β] (f : α → β),
  IsUniformEmbedding f ↔ IsUniformInducing f ∧ Function.Injective f
Defined in
Mathlib.Topology.UniformSpace.Defs
Cited by
4 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
UniformSpaceUniformSpace
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Around this declaration

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

isUniformEmbedding_iff' · cited by 3isUniformEmbedding_iff'Filter.HasBasis.isUniformEmbedding_iff' · cited by 1HasBasis.isUniformEmbeddi…Metric.isUniformEmbedding_iff · cited by 0Metric.isUniformEmbedding…EMetric.isUniformEmbedding_iff · cited by 0EMetric.isUniformEmbeddin…UniformSpace · cited by 2040UniformSpaceIsUniformInducing · cited by 128IsUniformInducingIsUniformEmbedding · cited by 107IsUniformEmbeddingIsUniformEmbedding.casesOn · cited by 1IsUniformEmbedding.casesOnisUniformEmbedding_iffCITED BYCITES

Cites4

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Cited by4

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