Theorems · Theorem · order theory

PredOrder.accPt_principal

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α] [PredOrder α] [NoMinOrder α]
  {a : α} {s : Set α}, AccPt a (Filter.principal s) ↔ ¬IsMax a ∧ ∀ (b : α), a < b → (s ∩ Set.Ioo a b).Nonempty

Defined in

Mathlib.Topology.Order.SuccPred

Cited by

2 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderTopologicalSpaceOrderTopologyPredOrderNoMinOrder