Theorems · Theorem · general topology
TopologicalSpace.Compacts.isOpen_setOfPred_disjoint_coe
∀ {α : Type u_1} [inst : TopologicalSpace α] [T2Space α], IsOpen {p | Disjoint ↑p.1 ↑p.2}- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT2Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- SetLike.coestatement and proof · cited by 8,199
- Set.ofPredstatement and proof · cited by 6,101
- IsOpenstatement and proof · cited by 2,400
- Disjointstatement and proof · cited by 2,201
- SProd.sprodproof · cited by 1,750
- T2Spacestatement and proof · cited by 1,351
- TopologicalSpace.Compactsstatement and proof · cited by 386
- IsOpen.prodproof · cited by 22
- TopologicalSpace.Compacts.isCompactproof · cited by 18
- isOpen_iff_forall_mem_openproof · cited by 18
Cited by3
Results whose statement or proof uses this declaration.
- TopologicalSpace.Compacts.isOpen_setOfPred_disjointproof · cited by 1
- TopologicalSpace.NonemptyCompacts.isOpen_setOfPred_disjoint_coeproof · cited by 1
- TopologicalSpace.Compacts.isOpen_setOf_disjoint_coeproof · cited by 0