Theorems · Theorem · general topology

isOpen_isPathConnected_basis

∀ {X : Type u_1} [inst : TopologicalSpace X] [LocallyPathConnectedSpace X] (x : X),
  (nhds x).HasBasis (fun s => IsOpen s ∧ x ∈ s ∧ IsPathConnected s) id

Defined in

Mathlib.Topology.Connected.LocallyPathConnected

Cited by

0 results in Mathlib

Foundations

Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLocallyPathConnectedSpace