Theorems · Theorem · general topology
upperSemicontinuousWithinAt_iff_limsup_le
∀ {α : Type u_1} [inst : TopologicalSpace α] {s : Set α} {x : α} {γ : Type u_4} [inst_1 : CompleteLinearOrder γ]
{f : α → γ}, UpperSemicontinuousWithinAt f s x ↔ Filter.limsup f (nhdsWithin x s) ≤ f x- Defined in
- Mathlib.Topology.Semicontinuity.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- nhdsWithinstatement · cited by 1,912
- Filter.limsupstatement · cited by 226
- CompleteLinearOrderstatement and proof · cited by 126
- UpperSemicontinuousWithinAtstatement · cited by 44
- lowerSemicontinuousWithinAt_iff_le_liminfproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- UpperSemicontinuousWithinAt.limsup_leproof · cited by 0