Theorems · Theorem · order theory
Topology.IsScott.scott_eq_upper_of_completeLinearOrder
∀ {α : Type u_1} [inst : CompleteLinearOrder α], Topology.scott α Set.univ = Topology.upper α- Defined in
- Mathlib.Topology.Order.ScottTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLinearOrder
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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
- Set.univstatement and proof · cited by 3,945
- Compl.complproof · cited by 2,925
- IsOpenproof · cited by 2,400
- Set.Iicproof · cited by 1,111
- CompleteLinearOrderstatement and proof · cited by 126
- TopologicalSpace.extproof · cited by 15
- Topology.scottstatement and proof · cited by 9
- Topology.upperstatement and proof · cited by 5
- Topology.IsUpper.isTopologicalSpace_basisproof · cited by 1
- Topology.IsScott.isOpen_iff_Iic_compl_or_univproof · cited by 1
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