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Theorems · Theorem · general topology

lowerHemicontinuousOn_iff

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → Set β} {s : Set α},
  LowerHemicontinuousOn f s ↔ ∀ x ∈ s, LowerHemicontinuousWithinAt f s x
Defined in
Mathlib.Topology.Semicontinuity.Defs
Cited by
1 results in Mathlib
Foundations
Depth 52 from the axioms · uses propext, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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Around this declaration

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TendstoUniformlyOn.lowerHemicontinuousOn · cited by 1TendstoUniformlyOn.lowerH…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceLowerHemicontinuousWithinAt · cited by 15LowerHemicontinuousWithin…LowerHemicontinuousOn · cited by 14LowerHemicontinuousOnlowerHemicontinuousOn_iffCITED BYCITES

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Cited by1

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