Theorems · Theorem · general topology

LocallyPathConnectedSpace.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 → IsPathConnected (s x i)) → LocallyPathConnectedSpace X

Defined in

Mathlib.Topology.Connected.LocallyPathConnected

Cited by

2 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpace