Mathlib Map

Theorems · Theorem · general topology

IsDenseEmbedding.injective

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {e : α → β},
  IsDenseEmbedding e → Function.Injective e

A dense embedding is injective.

Defined in
Mathlib.Topology.DenseEmbedding
Cited by
6 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
TopologicalSpaceTopologicalSpace
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Around this declaration

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

IsDenseEmbedding.subtype · cited by 3IsDenseEmbedding.subtypeisUniformEmbedding_subtypeEmb · cited by 1isUniformEmbedding_subtyp…IsDenseEmbedding.isEmbedding · cited by 1IsDenseEmbedding.isEmbedd…UniformSpace.Completion.coe_inv · cited by 0Completion.coe_invIsDenseEmbedding.inj_iff · cited by 0IsDenseEmbedding.inj_iffIsDenseEmbedding.prodMap · cited by 0IsDenseEmbedding.prodMapTopologicalSpace · cited by 24529TopologicalSpaceIsDenseEmbedding · cited by 24IsDenseEmbeddingIsDenseEmbedding.injectiveCITED BYCITES

Cites2

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Cited by6

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