connectedComponentIn_mem_nhds

∀ {α : Type u} [inst : TopologicalSpace α] [LocallyConnectedSpace α] {F : Set α} {x : α},
  F ∈ nhds x → connectedComponentIn F x ∈ nhds x

Defined in: Mathlib.Topology.Connected.LocallyConnected
Cited by: 2 results in Mathlib
Foundations: Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace LocallyConnectedSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.