Theorems · Theorem · general topology

Topology.IsQuotientMap.of_surjective_continuous

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [CompactSpace X] [T2Space Y]
  {f : X → Y}, Function.Surjective f → Continuous f → Topology.IsQuotientMap f

A continuous surjective map from a compact space to a Hausdorff space is a quotient map.

Defined in

Mathlib.Topology.Separation.Hausdorff

Cited by

0 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceCompactSpaceT2Space