Theorems · Theorem · general topology
TopologicalSpace.Closeds.isUniformEmbedding_singleton
∀ {α : Type u_1} [inst : UniformSpace α] [inst_1 : T0Space α], IsUniformEmbedding fun x => {x}- Defined in
- Mathlib.Topology.UniformSpace.Closeds
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpaceT0Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- UniformSpacestatement and proof · cited by 2,040
- T0Spacestatement and proof · cited by 179
- TopologicalSpace.Closedsstatement · cited by 168
- IsUniformEmbeddingstatement · cited by 107
- IsUniformEmbedding.of_comp_iffproof · cited by 8
- TopologicalSpace.Closeds.isUniformEmbedding_coeproof · cited by 6
- UniformSpace.hausdorff.isUniformEmbedding_singletonproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- TopologicalSpace.Closeds.isEmbedding_singletonproof · cited by 1
- TopologicalSpace.Closeds.discreteUniformity_iffproof · cited by 0
- TopologicalSpace.Closeds.isClosedEmbedding_singletonproof · cited by 0
- TopologicalSpace.Closeds.uniformContinuous_singletonproof · cited by 0