Theorems · Definition · general topology
Homeomorph.funUnique
(ι : Type u_7) → (X : Type u_8) → [Unique ι] → [inst : TopologicalSpace X] → (ι → X) ≃ₜ X
If ι has a unique element, then ι → X is homeomorphic to X.
- Defined in
- Mathlib.Topology.Homeomorph.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniqueTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Uniquestatement and proof · cited by 400
- Equiv.funUniqueproof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- ContinuousLinearEquiv.funUniqueproof · cited by 3
- Homeomorph.funUnique_applystatement and proof · cited by 0
- Homeomorph.funUnique_symm_applystatement and proof · cited by 0