Theorems · Definition · general topology
TopologicalSpace.Compacts.equiv
{α : Type u_1} →
{β : Type u_2} →
[inst : TopologicalSpace α] →
[inst_1 : TopologicalSpace β] → α ≃ₜ β → TopologicalSpace.Compacts α ≃ TopologicalSpace.Compacts βA homeomorphism induces an equivalence on compact sets, by taking the image.
- Defined in
- Mathlib.Topology.Sets.Compacts
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Equivstatement · cited by 8,337
- Homeomorphstatement and proof · cited by 725
- TopologicalSpace.Compactsstatement and proof · cited by 386
- Homeomorph.symmproof · cited by 365
- Homeomorph.continuousproof · cited by 53
- TopologicalSpace.Compacts.mapproof · cited by 37
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.Content.innerContent_comapproof · cited by 3
- TopologicalSpace.Compacts.equiv_transstatement · cited by 0
- TopologicalSpace.Compacts.equiv_applystatement and proof · cited by 0
- TopologicalSpace.Compacts.equiv_reflstatement · cited by 0
- TopologicalSpace.Compacts.equiv_symmstatement · cited by 0
- TopologicalSpace.Compacts.equiv_symm_applystatement and proof · cited by 0
- TopologicalSpace.Compacts.coe_equiv_apply_eq_preimagestatement · cited by 0