Theorems · Definition · general topology

Topology.IsQuotientMap.lift

{X : Type u_1} →
  {Y : Type u_2} →
    {Z : Type u_3} →
      [inst : TopologicalSpace X] →
        [inst_1 : TopologicalSpace Y] →
          [inst_2 : TopologicalSpace Z] →
            {f : C(X, Y)} → Topology.IsQuotientMap ⇑f → (g : C(X, Z)) → Function.FactorsThrough ⇑g ⇑f → C(Y, Z)

Descend a continuous map, which is constant on the fibres, along a quotient map.

Defined in

Mathlib.Topology.ContinuousMap.Basic

Cited by

6 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace