Theorems · Theorem · general topology

Topology.IsLower.isTopologicalBasis_insert_univ_subbasis

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [Topology.IsLower α],
  TopologicalSpace.IsTopologicalBasis (insert Set.univ {s | ∃ a, (Set.Ici a)ᶜ = s})

Defined in: Mathlib.Topology.Order.LowerUpperTopology
Cited by: 2 results in Mathlib
Foundations: Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder TopologicalSpace Topology.IsLower

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Cites15

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
LinearOrderstatement and proof · cited by 8,572
Set.ofPredstatement and proof · cited by 6,101
Set.univstatement · cited by 3,945
Compl.complstatement and proof · cited by 2,925
Set.Iioproof · cited by 1,166
Set.Icistatement and proof · cited by 1,070
TopologicalSpace.IsTopologicalBasisstatement · cited by 126
TopologicalSpace.generateFromproof · cited by 62
Topology.IsLowerstatement and proof · cited by 24
Set.compl_Iciproof · cited by 11

Cited by2

Results whose statement or proof uses this declaration.

Topology.IsLower.isTopologicalSpace_basisproof · cited by 1
Topology.IsUpper.isTopologicalBasis_insert_univ_subbasisproof · cited by 0