Theorems · Theorem · general topology
Homeomorph.comp_continuousAt_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) (z : Z), ContinuousAt (⇑h ∘ f) z ↔ ContinuousAt f z- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 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
- Homeomorphstatement and proof · cited by 725
- ContinuousAtstatement · cited by 697
- Homeomorph.isInducingproof · cited by 33
- Topology.IsInducing.continuousAt_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- continuousAt_neg_iffproof · cited by 1
- continuousAt_inv_iffproof · cited by 1