Theorems · Theorem · general topology
upperHemicontinuousOn_iff_restrict
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → Set β} {s : Set α},
UpperHemicontinuous (s.domRestrict f) ↔ UpperHemicontinuousOn f s- Defined in
- Mathlib.Topology.Semicontinuity.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Elemstatement · cited by 7,166
- Set.domRestrictstatement · cited by 383
- UpperHemicontinuousstatement · cited by 30
- UpperHemicontinuousOnstatement · cited by 21
- semicontinuous_restrict_iffproof · cited by 4
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