Theorems · Theorem · general topology
LowerSemicontinuousWithinAt.le_liminf
∀ {α : Type u_1} [inst : TopologicalSpace α] {s : Set α} {x : α} {γ : Type u_4} [inst_1 : CompleteLinearOrder γ]
{f : α → γ}, LowerSemicontinuousWithinAt f s x → f x ≤ Filter.liminf f (nhdsWithin x s)Alias of the forward direction of lowerSemicontinuousWithinAt_iff_le_liminf.
- Defined in
- Mathlib.Topology.Semicontinuity.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
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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.liminfstatement · cited by 198
- CompleteLinearOrderstatement and proof · cited by 126
- LowerSemicontinuousWithinAtstatement · cited by 44
- lowerSemicontinuousWithinAt_iff_le_liminfproof · cited by 3
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