Theorems · Theorem · general topology

Topology.IsLower.isTopologicalBasis

∀ {α : Type u_1} [inst : Preorder α] [inst_1 : TopologicalSpace α] [Topology.IsLower α],
  TopologicalSpace.IsTopologicalBasis (Topology.IsLower.lowerBasis α)

Defined in: Mathlib.Topology.Order.LowerUpperTopology
Cited by: 3 results in Mathlib
Foundations: Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Preorder TopologicalSpace Topology.IsLower

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Cites31

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setproof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Preorderstatement and proof · cited by 7,952
Set.Elemproof · cited by 7,166
Set.ofPredproof · cited by 6,101
Set.imageproof · cited by 5,609
Set.rangeproof · cited by 4,705
Finiteproof · cited by 3,029
Compl.complproof · cited by 2,925
Set.iUnionproof · cited by 2,483
Set.extproof · cited by 2,266
Set.Finiteproof · cited by 1,814

Cited by3

Results whose statement or proof uses this declaration.

PrimitiveSpectrum.isTopologicalBasis_relativeLowerproof · cited by 1
Topology.IsUpper.isTopologicalBasisproof · cited by 0
Topology.IsLawson.isTopologicalBasisproof · cited by 0