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Theorems · Theorem · general topology

isPreconnected_singleton

∀ {α : Type u} [inst : TopologicalSpace α] {x : α}, IsPreconnected {x}
Defined in
Mathlib.Topology.Connected.Basic
Cited by
3 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.

mem_connectedComponent · cited by 21mem_connectedComponentTopologicalSpace.NonemptyCompacts.locallyConnectedSpace_iff · cited by 1NonemptyCompacts.locallyC…Set.Subsingleton.isPreconnected · cited by 0Subsingleton.isPreconnect…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceIsPreconnected · cited by 205IsPreconnectedIsConnected.isPreconnected · cited by 36IsConnected.isPreconnectedisConnected_singleton · cited by 2isConnected_singletonisPreconnected_singletonCITED BYCITES

Cites5

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Cited by3

Results whose statement or proof uses this declaration.