Theorems · Definition · general topology
Homeomorph.Set.univ
(X : Type u_7) → [inst : TopologicalSpace X] → ↑Set.univ ≃ₜ X
Set.univ X is homeomorphic to X.
- Defined in
- Mathlib.Topology.Homeomorph.Lemmas
- Cited by
- 16 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Equivproof · cited by 8,337
- Set.Elemstatement and proof · cited by 7,166
- Set.univstatement and proof · cited by 3,945
- Homeomorphstatement · cited by 725
- Equiv.Set.univproof · cited by 21
Cited by18
Results whose statement or proof uses this declaration.
- Homeomorph.unitBallproof · cited by 4
- Bundle.Trivialization.preimageHomeomorphproof · cited by 2
- OpenPartialHomeomorph.isOpenEmbeddingproof · cited by 2
- IsCoveringMapOn.of_isCoveringMap_subtypeproof · cited by 1
- ProperSMul.isProperMap_smul_pair_setproof · cited by 1
- Topology.IsOpenEmbedding.isLocalHomeomorphproof · cited by 1
- AddSubgroup.discrete_iff_addCyclicproof · cited by 1
- ProperVAdd.isProperMap_vadd_pair_setproof · cited by 1
- Module.isLocallyConstant_rankAtStalkproof · cited by 1
- IsLocalHomeomorph.discreteTopology_range_iffproof · cited by 1
- Subgroup.discrete_iff_cyclicproof · cited by 0
- TopologicalSpace.noetherian_univ_iffproof · cited by 0