Mathlib Map

Theorems · Theorem · general topology

nhds_inf_atTop

∀ {α : Type u} [inst : Preorder α] [NoTopOrder α] [inst_2 : TopologicalSpace α] [ClosedIciTopology α] (a : α),
  nhds a ⊓ Filter.atTop = ⊥
Defined in
Mathlib.Topology.Order.OrderClosed
Cited by
1 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderNoTopOrderTopologicalSpaceClosedIciTopology
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

inf_nhds_atTop · cited by 0inf_nhds_atTopTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121FilterPreorder · cited by 7952Preordernhds · cited by 5554nhdsBot.bot · cited by 4720Bot.botFilter.atTop · cited by 2405Filter.atTopClosedIciTopology · cited by 156ClosedIciTopologyDisjoint.eq_bot · cited by 52Disjoint.eq_botNoTopOrder · cited by 50NoTopOrderdisjoint_nhds_atTop · cited by 4disjoint_nhds_atTopnhds_inf_atTopCITED BYCITES

Cites10

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

Cited by1

Results whose statement or proof uses this declaration.