Theorems · Theorem · order theory
Topology.IsScott.closure_singleton
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : TopologicalSpace α] {a : α} [Topology.IsScott α Set.univ],
closure {a} = Set.Iic aThe closure of a singleton {a} in the Scott topology is the right-closed left-infinite interval
(-∞,a].
- Defined in
- Mathlib.Topology.Order.ScottTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
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.coeproof · cited by 8,199
- Preorderstatement and proof · cited by 7,952
- Set.univstatement and proof · cited by 3,945
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- closurestatement and proof · cited by 1,254
- Set.Iicstatement · cited by 1,111
- LowerSetproof · cited by 230
- Set.singleton_subset_iffproof · cited by 206
- closure_minimalproof · cited by 94
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