Theorems · Theorem · general topology
Homeomorph.comp_continuous_iff
∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_4} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
[inst_2 : TopologicalSpace Z] (h : X ≃ₜ Y) {f : Z → X}, Continuous (⇑h ∘ f) ↔ Continuous f- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 5 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.
Cites6
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
- Topology.IsInducing.continuous_iffproof · cited by 34
- Homeomorph.isInducingproof · cited by 33
Cited by5
Results whose statement or proof uses this declaration.
- continuous_inv_iffproof · cited by 1
- continuous_neg_iffproof · cited by 1
- ContinuousAlgEquiv.comp_continuous_iffproof · cited by 0
- IsometryEquiv.comp_continuous_iffproof · cited by 0
- ContinuousLinearEquiv.comp_continuous_iffproof · cited by 0