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Theorems · Theorem · general topology

subsingleton_of_preconnected_totallyDisconnected

∀ {α : Type u} [inst : TopologicalSpace α] [PreconnectedSpace α] [TotallyDisconnectedSpace α], Subsingleton α
Defined in
Mathlib.Topology.Connected.TotallyDisconnected
Cited by
1 results in Mathlib
Foundations
Depth 10 from the axioms · uses no axioms
Assumes
TopologicalSpacePreconnectedSpaceTotallyDisconnectedSpace
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Around this declaration

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

IsPreconnected.isDiscrete_iff_subsingleton · cited by 0IsPreconnected.isDiscrete…TopologicalSpace · cited by 24529TopologicalSpaceTotallyDisconnectedSpace · cited by 295TotallyDisconnectedSpacePreconnectedSpace · cited by 64PreconnectedSpacePreconnectedSpace.isPreconnected_univ · cited by 26PreconnectedSpace.isPreco…IsPreconnected.subsingleton · cited by 6IsPreconnected.subsinglet…Set.subsingleton_of_univ_subsingleton · cited by 3Set.subsingleton_of_univ_…subsingleton_of_preconnected_…CITED BYCITES

Cites6

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Cited by1

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