Theorems · Theorem · global analysis

Manifold.locallyCompact_of_finiteDimensional

∀ {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) [LocallyCompactSpace 𝕜] [FiniteDimensional 𝕜 E], LocallyCompactSpace M

A finite-dimensional manifold modelled on a locally compact field (such as ℝ, ℂ or the p-adic numbers) is locally compact.

Defined in

Mathlib.Geometry.Manifold.IsManifold.ExtChartAt

Cited by

0 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceLocallyCompactSpaceFiniteDimensional