Theorems · Theorem · general topology

pi_Icc_mem_nhds

∀ {ι : Type u_1} {X : ι → Type u_2} [Finite ι] [inst : (i : ι) → LinearOrder (X i)]
  [inst_1 : (i : ι) → TopologicalSpace (X i)] [∀ (i : ι), OrderTopology (X i)] {a b x : (i : ι) → X i},
  (∀ (i : ι), a i < x i) → (∀ (i : ι), x i < b i) → Set.Icc a b ∈ nhds x

Defined in

Mathlib.Topology.Order.Basic

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FiniteLinearOrderTopologicalSpaceOrderTopology