Theorems · Theorem · general topology
isOpen_iSup_iff
∀ {α : Type u} {ι : Sort v} {t : ι → TopologicalSpace α} {s : Set α}, IsOpen s ↔ ∀ (i : ι), IsOpen s- Defined in
- Mathlib.Topology.Order
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Set.ofPredproof · cited by 6,101
- iSupstatement · cited by 2,415
- IsOpenstatement and proof · cited by 2,400
- setOfPred_isOpen_iSupproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- TopCat.isOpen_iff_of_isColimitproof · cited by 4
- isOpen_sigma_iffproof · cited by 4
- FiberPrebundle.isOpen_sourceproof · cited by 1
- alexandrovDiscrete_iSupproof · cited by 0