Theorems · Definition · general topology
Homeomorph.setCongr
{X : Type u_1} → [inst : TopologicalSpace X] → {s t : Set X} → s = t → ↑s ≃ₜ ↑tIf two sets are equal, then they are homeomorphic.
- Defined in
- Mathlib.Topology.Homeomorph.Lemmas
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Equivproof · cited by 8,337
- Set.Elemstatement and proof · cited by 7,166
- Homeomorphstatement · cited by 725
- Equiv.setCongrproof · cited by 13
Cited by41
Results whose statement or proof uses this declaration.
- Profinite.NobelingProof.ProjRestrictsproof · cited by 12
- cfcₙAuxproof · cited by 11
- Topology.IsQuotientMap.isStrictMap_iffproof · cited by 8
- AlgebraicGeometry.Scheme.Hom.fiberHomeoproof · cited by 6
- iccHomeoIproof · cited by 5
- FiberBundle.homeomorphAtproof · cited by 4
- Topology.IsEmbedding.homeomorphImageproof · cited by 3
- continuous_cfcₙAuxproof · cited by 3
- Topology.IsEmbedding.homeomorphOfSubsetRangeproof · cited by 2
- AddMonoidHom.isStrictMap_prodMap_iffproof · cited by 2
- RCLike.nonUnitalContinuousFunctionalCalculusproof · cited by 2
- ContinuousLinearMap.isStrictMap_isClosed_range_iff_restrictproof · cited by 2