Theorems · Theorem · general topology
UpperSemicontinuousWithinAt.mono
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : Preorder β] {f : α → β} {x : α} {s t : Set α},
UpperSemicontinuousWithinAt f s x → t ⊆ s → UpperSemicontinuousWithinAt f t x- Defined in
- Mathlib.Topology.Semicontinuity.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpacePreorder
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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
- UpperSemicontinuousWithinAtstatement and proof · cited by 44
- SemicontinuousWithinAt.monoproof · cited by 5
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