Theorems · Theorem · general topology

StronglyLocallyContractibleSpace.of_bases

∀ {X : Type u_1} [inst : TopologicalSpace X] {ι : Type u_3} {p : X → ι → Prop} {s : X → ι → Set X},
  (∀ (x : X), (nhds x).HasBasis (p x) (s x)) →
    (∀ (x : X) (i : ι), p x i → ContractibleSpace ↑(s x i)) → StronglyLocallyContractibleSpace X

A helper to construct a strongly locally contractible space from a neighborhood basis where each basis element is contractible as a subspace.

Defined in

Mathlib.Topology.Homotopy.LocallyContractible

Cited by

1 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpace