Theorems · Theorem · general topology
upperHemicontinuousWithinAt_univ_iff
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → Set β} {x : α},
UpperHemicontinuousWithinAt f Set.univ x ↔ UpperHemicontinuousAt f x- Defined in
- Mathlib.Topology.Semicontinuity.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.univstatement · cited by 3,945
- UpperHemicontinuousWithinAtstatement · cited by 22
- UpperHemicontinuousAtstatement · cited by 21
- semicontinuousWithinAt_univ_iffproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- upperHemicontinuousAt_iff_frequentlyproof · cited by 2
- UpperHemicontinuousAt.unionproof · cited by 1
- UpperHemicontinuousAt.interproof · cited by 1