Theorems · Theorem · general topology

Topology.IsLower.topology_eq

∀ (α : Type u_1) [inst : Preorder α] [inst_1 : TopologicalSpace α] [Topology.IsLower α], inst_1 = Topology.lower α

Defined in: Mathlib.Topology.Order.LowerUpperTopology
Cited by: 5 results in Mathlib
Foundations: Depth 10 from the axioms · uses no axioms
Assumes: Preorder TopologicalSpace Topology.IsLower

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Cites5

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

TopologicalSpacestatement and proof · cited by 24,529
Preorderstatement and proof · cited by 7,952
Topology.IsLowerstatement and proof · cited by 24
Topology.lowerstatement · cited by 7
Topology.IsLower.topology_eq_lowerTopologyproof · cited by 2

Cited by5

Results whose statement or proof uses this declaration.

Topology.IsLower.isTopologicalBasisproof · cited by 3
Topology.IsLower.continuous_iff_Iciproof · cited by 2
Topology.IsLower.isTopologicalBasis_insert_univ_subbasisproof · cited by 2
Topology.IsLower.isOpen_iff_generate_Ici_complproof · cited by 1
Topology.IsLower.scottHausdorff_leproof · cited by 0