Theorems · Theorem · general topology

isTotallyDisconnected_of_totallyDisconnectedSpace

∀ {α : Type u} [inst : TopologicalSpace α] [TotallyDisconnectedSpace α] (s : Set α), IsTotallyDisconnected s

Defined in: Mathlib.Topology.Connected.TotallyDisconnected
Cited by: 0 results in Mathlib
Foundations: Depth 9 from the axioms · uses no axioms
Assumes: TopologicalSpace TotallyDisconnectedSpace

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

Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
TotallyDisconnectedSpacestatement and proof · cited by 295
Set.subset_univproof · cited by 228
IsPreconnectedproof · cited by 205
IsTotallyDisconnectedstatement · cited by 14
TotallyDisconnectedSpace.isTotallyDisconnected_univproof · cited by 3

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