Theorems · Theorem · general topology
LowerSemicontinuousAt.lowerSemicontinuousWithinAt
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : Preorder β] {f : α → β} {x : α} (s : Set α),
LowerSemicontinuousAt f x → LowerSemicontinuousWithinAt f s x- Defined in
- Mathlib.Topology.Semicontinuity.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpacePreorder
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
- Preorderstatement and proof · cited by 7,952
- LowerSemicontinuousWithinAtstatement · cited by 44
- LowerSemicontinuousAtstatement and proof · cited by 37
- SemicontinuousAt.semicontinuousWithinAtproof · cited by 9
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.