Theorems · Theorem · general topology

mem_nhdsGE_iff_exists_Icc_subset

∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] [NoMaxOrder α]
  [DenselyOrdered α] {a : α} {s : Set α}, s ∈ nhdsWithin a (Set.Ici a) ↔ ∃ u, a < u ∧ Set.Icc a u ⊆ s

A set is a neighborhood of a within [a, +∞) if and only if it contains an interval [a, u] with a < u.

Defined in

Mathlib.Topology.Order.LeftRightNhds

Cited by

1 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLinearOrderOrderTopologyNoMaxOrderDenselyOrdered