Mathlib Map

Theorems · Theorem · general topology

IsUniformInducing.isUniformEmbedding

∀ {α : Type u} {β : Type v} [inst : UniformSpace α] [inst_1 : UniformSpace β] [T0Space α] {f : α → β},
  IsUniformInducing f → IsUniformEmbedding f

If the domain of a IsUniformInducing map f is a T₀ space, then f is injective, hence it is a IsUniformEmbedding.

Defined in
Mathlib.Topology.UniformSpace.UniformEmbedding
Cited by
3 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceUniformSpaceT0Space
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

isUniformEmbedding_of_spaced_out · cited by 2isUniformEmbedding_of_spa…isUniformEmbedding_iff_isUniformInducing · cited by 2isUniformEmbedding_iff_is…isClosedEmbedding_cfcₙHom_of_cfcHom · cited by 0isClosedEmbedding_cfcₙHom…UniformSpace · cited by 2040UniformSpaceT0Space · cited by 179T0SpaceIsUniformInducing · cited by 128IsUniformInducingIsUniformEmbedding · cited by 107IsUniformEmbeddingIsUniformInducing.isInducing · cited by 23IsUniformInducing.isInduc…Topology.IsInducing.injective · cited by 3IsInducing.injectiveIsUniformInducing.isUniformEm…CITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.