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Theorems · Theorem · general topology

IsPathConnected.subset_pathComponentIn

∀ {X : Type u_1} [inst : TopologicalSpace X] {x : X} {F s : Set X},
  IsPathConnected s → x ∈ s → s ⊆ F → s ⊆ pathComponentIn F x
Defined in
Mathlib.Topology.Connected.PathConnected
Cited by
2 results in Mathlib
Foundations
Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
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Around this declaration

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

IsOpen.pathComponentIn · cited by 5IsOpen.pathComponentInLocallyPathConnectedSpace.coinduced · cited by 2LocallyPathConnectedSpace…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceIsPathConnected · cited by 65IsPathConnectedpathComponentIn · cited by 19pathComponentInIsPathConnected.joinedIn · cited by 8IsPathConnected.joinedInJoinedIn.mono · cited by 2JoinedIn.monoIsPathConnected.subset_pathCo…CITED BYCITES

Cites6

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Cited by2

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