Theorems · Theorem · general topology

Topology.IsInducing.locallyCompactSpace

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [LocallyCompactSpace Y]
  {f : X → Y}, Topology.IsInducing f → IsLocallyClosed (Set.range f) → LocallyCompactSpace X

If f is a topology inducing map with a locally compact codomain and a locally closed range, then the domain of f is a locally compact space.

Defined in

Mathlib.Topology.Compactness.LocallyCompact

Cited by

4 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceLocallyCompactSpace