Theorems · Theorem · general topology

Topology.IsUpper.isTopologicalBasis_insert_univ_subbasis

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

Defined in: Mathlib.Topology.Order.LowerUpperTopology
Cited by: 0 results in Mathlib
Foundations: Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder TopologicalSpace Topology.IsUpper

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Setstatement · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
LinearOrderstatement and proof · cited by 8,572
Set.ofPredstatement · cited by 6,101
Set.univstatement · cited by 3,945
Compl.complstatement · cited by 2,925
Set.Iicstatement · cited by 1,111
TopologicalSpace.IsTopologicalBasisstatement · cited by 126
Topology.IsUpperstatement and proof · cited by 18
Topology.IsLower.isTopologicalBasis_insert_univ_subbasisproof · cited by 2

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