Theorems · Theorem · general topology
Semicontinuous.isOpen
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] {r : α → β → Prop},
Semicontinuous r → ∀ (b : β), IsOpen {x | r x b}- Defined in
- Mathlib.Topology.Semicontinuity.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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.
- TopologicalSpacestatement and proof · cited by 24,529
- Set.ofPredstatement · cited by 6,101
- IsOpenstatement · cited by 2,400
- Semicontinuousstatement and proof · cited by 12
- semicontinuous_iff_isOpenproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- continuousOn_cfcₙ_setProd_nhdsSetproof · cited by 0
- continuousOn_cfc_setProd_nhdsSetproof · cited by 0
- continuousOn_cfcₙ_nnreal_setProd_nhdsSetproof · cited by 0
- continuousOn_cfc_nnreal_setProd_nhdsSetproof · cited by 0