Theorems · Theorem · general topology
Homeomorph.compactSpace
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [CompactSpace X] (h : X ≃ₜ Y),
CompactSpace Y- Defined in
- Mathlib.Topology.Homeomorph.Lemmas
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- TopologicalSpacestatement and proof · cited by 24,529
- Homeomorphstatement and proof · cited by 725
- CompactSpacestatement and proof · cited by 593
- Homeomorph.symmproof · cited by 365
- isCompact_univproof · cited by 53
- Homeomorph.isCompact_preimageproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- ArzelaAscoli.isCompact_of_equicontinuousproof · cited by 2
- CompHaus.epi_iff_surjectiveproof · cited by 2
- AlgebraicGeometry.quasiCompact_affineProperty_iff_quasiSeparatedSpaceproof · cited by 1
- AlgebraicGeometry.Scheme.OpenCover.compactSpaceproof · cited by 0