Theorems · Theorem · general topology
IsOpen.exists_positiveCompacts_closure_subset
∀ {α : Type u_1} [inst : TopologicalSpace α] [R1Space α] [LocallyCompactSpace α] {U : Set α},
IsOpen U → U.Nonempty → ∃ K, closure ↑K ⊆ U- Defined in
- Mathlib.Topology.Sets.Compacts
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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.Nonemptystatement and proof · cited by 2,627
- IsOpenstatement and proof · cited by 2,400
- closurestatement and proof · cited by 1,254
- LocallyCompactSpacestatement and proof · cited by 324
- R1Spacestatement and proof · cited by 125
- TopologicalSpace.PositiveCompactsstatement and proof · cited by 112
- TopologicalSpace.PositiveCompacts.isCompactproof · cited by 21
- IsCompact.closure_subset_of_isOpenproof · cited by 9
- exists_positiveCompacts_subsetproof · cited by 1
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