Theorems · Theorem · global analysis

ModelWithCorners.t1Space

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] (I : ModelWithCorners 𝕜 E H) (M : Type u_4)
  [inst : TopologicalSpace M] [ChartedSpace H M], T1Space M

Every manifold is a Fréchet space (T1 space) -- regardless of whether it is Hausdorff.

Defined in

Mathlib.Geometry.Manifold.IsManifold.Basic

Cited by

5 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpace