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Theorems · Theorem · general topology

totallyDisconnectedSpace_iff

∀ (α : Type u) [inst : TopologicalSpace α], TotallyDisconnectedSpace α ↔ IsTotallyDisconnected Set.univ
Defined in
Mathlib.Topology.Connected.TotallyDisconnected
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
TopologicalSpace
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Around this declaration

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

Topology.IsEmbedding.isTotallyDisconnected_range · cited by 2IsEmbedding.isTotallyDisc…Homeomorph.totallyDisconnectedSpace · cited by 0Homeomorph.totallyDisconn…TopologicalSpace · cited by 24529TopologicalSpaceSet.univ · cited by 3945Set.univTotallyDisconnectedSpace · cited by 295TotallyDisconnectedSpaceIsTotallyDisconnected · cited by 14IsTotallyDisconnectedTotallyDisconnectedSpace.casesOn · cited by 1TotallyDisconnectedSpace.…totallyDisconnectedSpace_iffCITED BYCITES

Cites5

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Cited by2

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