Homeomorphisms

In this file we prove that local compactness is preserved by homeomorphisms.

Main results

• Homeomorph.locallyCompactSpace_iff : if the codomain of a homeomorphism is a locally compact space, then the domain is also a locally compact space.

theorem Homeomorph.locallyCompactSpace_iff {X : Type u_1} {Y : Type u_2} [TopologicalSpace X] [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.

Now part of mathlib.