Theorems · Theorem · general topology

Homeomorph.locallyCompactSpace_iff

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (h : X ≃ₜ Y),
  LocallyCompactSpace X ↔ LocallyCompactSpace Y

The codomain of a homeomorphism is a locally compact space if and only if the domain is a locally compact space.

Defined in

Mathlib.Topology.Homeomorph.Lemmas

Cited by

0 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace