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Theorems · Theorem · general topology

UpperHemicontinuous.upperHemicontinuousWithinAt

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → Set β},
  UpperHemicontinuous f → ∀ (s : Set α) (x : α), UpperHemicontinuousWithinAt f s x
Defined in
Mathlib.Topology.Semicontinuity.Defs
Cited by
1 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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upperHemicontinuousWithinAt_singleton_iff · cited by 2upperHemicontinuousWithin…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceUpperHemicontinuous · cited by 30UpperHemicontinuousUpperHemicontinuousWithinAt · cited by 22UpperHemicontinuousWithin…SemicontinuousAt.semicontinuousWithinAt · cited by 9SemicontinuousAt.semicont…UpperHemicontinuous.upperHemi…CITED BYCITES

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