Theorems · Theorem · general topology
Homeomorph.isStrictMap_comp_iff
∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
[inst_2 : TopologicalSpace Z] (e : X ≃ₜ Y) {f : Y → Z}, Topology.IsStrictMap (f ∘ ⇑e) ↔ Topology.IsStrictMap fStrict maps are preserved when precomposing with a homeomorphism.
- Defined in
- Mathlib.Topology.Maps.Strict.Basic
- Cited by
- 1 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
- Homeomorphstatement and proof · cited by 725
- Topology.IsStrictMapstatement · cited by 45
- Homeomorph.isQuotientMapproof · cited by 22
- Topology.IsQuotientMap.isStrictMap_iffproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Topology.Homeomorph.isStrictMap_comp_iffproof · cited by 0