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Theorems · Theorem · general topology

IsOpen.locPathConnectedSpace

Deprecated since 2026-06-21Use IsOpen.locallyPathConnectedSpace instead.

∀ {X : Type u_1} [inst : TopologicalSpace X] [LocallyPathConnectedSpace X] {U : Set X},
  IsOpen U → LocallyPathConnectedSpace ↑U

Alias of IsOpen.locallyPathConnectedSpace.

Defined in
Mathlib.Topology.Connected.LocallyPathConnected
Cited by
0 results in Mathlib
Foundations
Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceLocallyPathConnectedSpace
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Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Elem · cited by 7166Set.ElemIsOpen · cited by 2400IsOpenLocallyPathConnectedSpace · cited by 53LocallyPathConnectedSpaceIsOpen.locallyPathConnectedSpace · cited by 3IsOpen.locallyPathConnect…IsOpen.locPathConnectedSpaceCITED BYCITES

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