Theorems · Theorem · general topology
isClosed_iSup_iff
∀ {α : Type u} {ι : Sort v} {t : ι → TopologicalSpace α} {s : Set α}, IsClosed s ↔ ∀ (i : ι), IsClosed s- Defined in
- Mathlib.Topology.Order
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 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
- Compl.complproof · cited by 2,925
- iSupstatement · cited by 2,415
- IsOpenproof · cited by 2,400
- IsClosedstatement · cited by 1,639
- isOpen_compl_iffproof · cited by 63
Cited by1
Results whose statement or proof uses this declaration.
- SequentialSpace.iSupproof · cited by 1