Theorems · Theorem · global analysis

LocallyCompactSpace.of_locallyCompact_manifold

∀ {E : Type u_8} {𝕜 : Type u_9} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_10} [inst_3 : TopologicalSpace H] (M : Type u_11) [inst_4 : TopologicalSpace M]
  [ChartedSpace H M] (I : ModelWithCorners 𝕜 E H) [h : Nonempty M] [LocallyCompactSpace M], LocallyCompactSpace E

A locally compact manifold must be modelled on a locally compact space.

Defined in

Mathlib.Geometry.Manifold.IsManifold.ExtChartAt

Cited by

1 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNonemptyLocallyCompactSpace