Theorems · Theorem · general topology
LowerHemicontinuous.lowerHemicontinuousOn
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → Set β},
LowerHemicontinuous f → ∀ (s : Set α), LowerHemicontinuousOn f s- Defined in
- Mathlib.Topology.Semicontinuity.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- LowerHemicontinuousstatement and proof · cited by 21
- LowerHemicontinuousOnstatement · cited by 14
- Semicontinuous.semicontinuousOnproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- TendstoUniformly.lowerHemicontinuousproof · cited by 0