connectedComponent_eq_iInter_isClopen

∀ {X : Type u_1} [inst : TopologicalSpace X] [T2Space X] [CompactSpace X] (x : X), connectedComponent x = ⋂ s, ↑s

In a compact T₂ space, the connected component of a point equals the intersection of all its clopen neighbourhoods.

Defined in: Mathlib.Topology.Separation.Regular
Cited by: 2 results in Mathlib
Foundations: Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace T2Space CompactSpace

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