Theorems · Theorem · general topology
TopologicalSpace.Compacts.isOpen_setOf_disjoint_coe
Deprecated since 2026-07-09Use TopologicalSpace.Compacts.isOpen_setOfPred_disjoint_coe instead.
∀ {α : Type u_1} [inst : TopologicalSpace α] [T2Space α], IsOpen {p | Disjoint ↑p.1 ↑p.2}Alias of TopologicalSpace.Compacts.isOpen_setOfPred_disjoint_coe.
- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT2Space
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement · cited by 24,529
- SetLike.coestatement · cited by 8,199
- Set.ofPredstatement · cited by 6,101
- IsOpenstatement · cited by 2,400
- Disjointstatement · cited by 2,201
- T2Spacestatement · cited by 1,351
- TopologicalSpace.Compactsstatement · cited by 386
- TopologicalSpace.Compacts.isOpen_setOfPred_disjoint_coeproof · cited by 3
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