totallyDisconnectedSpace_iff_connectedComponent_singleton

∀ {α : Type u} [inst : TopologicalSpace α], TotallyDisconnectedSpace α ↔ ∀ (x : α), connectedComponent x = {x}

A space is totally disconnected iff its connected components are singletons.

Defined in: Mathlib.Topology.Connected.TotallyDisconnected
Cited by: 4 results in Mathlib
Foundations: Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace

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