Theorems · Theorem · general topology

exists_Icc_mem_subset_of_mem_nhdsGE

∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] {a : α} {s : Set α},
  s ∈ nhdsWithin a (Set.Ici a) → ∃ b, a ≤ b ∧ Set.Icc a b ∈ nhdsWithin a (Set.Ici a) ∧ Set.Icc a b ⊆ s

Defined in

Mathlib.Topology.Order.Basic

Cited by

2 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderTopology