locallyConnectedSpace_iff_connected_subsets

∀ {α : Type u} [inst : TopologicalSpace α],
  LocallyConnectedSpace α ↔ ∀ (x : α), ∀ U ∈ nhds x, ∃ V ∈ nhds x, IsPreconnected V ∧ V ⊆ U

Defined in: Mathlib.Topology.Connected.LocallyConnected
Cited by: 2 results in Mathlib
Foundations: Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace

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