Theorems · Theorem · general topology

ContinuousMap.isInducing_postcomp

∀ {X : Type u_2} {Y : Type u_3} {Z : Type u_4} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] (g : C(Y, Z)), Topology.IsInducing ⇑g → Topology.IsInducing g.comp

If g : C(Y, Z) is a topology inducing map, then the composition ContinuousMap.comp g : C(X, Y) → C(X, Z) is a topology inducing map too.

Defined in

Mathlib.Topology.CompactOpen

Cited by

2 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace