Theorems · Definition · general topology
Homeomorph.refl
(X : Type u_7) → [inst : TopologicalSpace X] → X ≃ₜ X
Identity map as a homeomorphism.
- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Equivproof · cited by 8,337
- Homeomorphstatement · cited by 725
- Equiv.reflproof · cited by 274
Cited by36
Results whose statement or proof uses this declaration.
- OpenPartialHomeomorph.reflproof · cited by 33
- TopCat.toSSetObjEquivproof · cited by 9
- NumberField.mixedEmbedding.mixedSpaceToRealMixedSpaceproof · cited by 6
- PartialHomeomorph.reflproof · cited by 5
- ContinuousMap.HomotopyEquiv.reflproof · cited by 3
- Bundle.Trivialization.transFiberHomeomorphproof · cited by 2
- Homeomorph.coe_reflstatement · cited by 2
- Bundle.Trivialization.preimageHomeomorphproof · cited by 2
- Bundle.Trivialization.preimageSingletonHomeomorphproof · cited by 2
- IsEvenlyCovered.homeomorph_compproof · cited by 2
- Homeomorph.refl_applystatement and proof · cited by 1
- Homeomorph.self_trans_symmstatement · cited by 1