Theorems · Theorem · general topology

Topology.IsEmbedding.isStrictMap_iff

∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] {f : X → Y} {g : Y → Z},
  Topology.IsEmbedding g → (Topology.IsStrictMap f ↔ Topology.IsStrictMap (g ∘ f))

Assume that g : Y → Z is an embedding. Then f : X → Y is strict if and only if g ∘ f is strict.

Defined in

Mathlib.Topology.Maps.Strict.Basic

Cited by

6 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace