Theorems · Theorem · general topology
Homeomorph.continuous
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (h : X ≃ₜ Y), Continuous ⇑h- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses Quot.sound
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.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement · cited by 2,592
- Homeomorphstatement and proof · cited by 725
- Homeomorph.continuous_toFunproof · cited by 4
Cited by57
Results whose statement or proof uses this declaration.
- Homeomorph.isInducingproof · cited by 33
- Homeomorph.isQuotientMapproof · cited by 22
- Homeomorph.isHomeomorphproof · cited by 19
- Homeomorph.preimage_closureproof · cited by 9
- MeasureTheory.Measure.Regular.mapproof · cited by 9
- TopologicalSpace.Compacts.equivproof · cited by 7
- Homeomorph.isProperMapproof · cited by 6
- Homeomorph.isOpenQuotientMapproof · cited by 5
- Homeomorph.measurableproof · cited by 5
- MeasureTheory.Content.innerContent_comapstatement and proof · cited by 3
- Homeomorph.toCocompactMapproof · cited by 3
- Homeomorph.preimage_frontierproof · cited by 3