Insertion theorems for maps to ordered topological vector spaces.

For an ordered topological vector space Y and a , b ∈ Y , we write a ≪ b if b − a is an interior point of the positive cone. Modifying the earlier results of Borwein–Théra, in this paper, ≪ is extended over Y • • = Y ∪ { ∞ } ∪ { − ∞ } and a natural topology on Y • • is introduced. For a topological space X , and a non-trivial separable ordered topological vector space Y with an interior point of the positive cone, we show the following: X is normal and countably paracompact if and only if for every lower semi-continuous map f : X → Y • • and every upper semi-continuous map g : X → Y • • with g ≪ f , there exists a continuous map h : X → Y such that g ≪ h ≪ f . [ABSTRACT FROM AUTHOR]