Theorems · Theorem · general topology
IsUniformEmbedding.isClosedEmbedding
∀ {α : Type u_1} {β : Type u_2} [inst : UniformSpace α] [inst_1 : UniformSpace β] [CompleteSpace α] [T0Space β]
{f : α → β}, IsUniformEmbedding f → Topology.IsClosedEmbedding f- Cited by
- 7 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CompleteSpacestatement and proof · cited by 2,532
- UniformSpacestatement and proof · cited by 2,040
- Topology.IsClosedEmbeddingstatement · cited by 195
- T0Spacestatement and proof · cited by 179
- IsUniformEmbeddingstatement and proof · cited by 107
- IsUniformEmbedding.isUniformInducingproof · cited by 33
- IsUniformEmbedding.isEmbeddingproof · cited by 25
- IsComplete.isClosedproof · cited by 6
- IsUniformInducing.isComplete_rangeproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- Filter.tendsto_ofReal_iffproof · cited by 5
- Filter.tendsto_ofReal_iff'proof · cited by 1
- SpectrumRestricts.isClosedEmbedding_starAlgHomproof · cited by 1
- QuasispectrumRestricts.isClosedEmbedding_nonUnitalStarAlgHomproof · cited by 1
- QuasispectrumRestricts.nonUnitalClosedEmbeddingCFCproof · cited by 0
- SpectrumRestricts.closedEmbeddingCFCproof · cited by 0
- isClosedEmbedding_cfcₙHom_of_cfcHomproof · cited by 0