Theorems · Theorem · manifolds

ChartedSpace.locallyCompactSpace

∀ (H : Type u) (M : Type u_2) [inst : TopologicalSpace H] [inst_1 : TopologicalSpace M] [ChartedSpace H M]
  [LocallyCompactSpace H], LocallyCompactSpace M

If a topological space admits an atlas with locally compact charts, then the space itself is locally compact.

Defined in

Mathlib.Geometry.Manifold.ChartedSpace

Cited by

5 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceChartedSpaceLocallyCompactSpace