Insertion theorems for maps to ordered topological vector spaces

摘要

For an ordered topological vector space Y and a, b is an element of Y, we write a b if b - a is an interior point of the positive cone. Modifying the earlier results of Borwein-Thera, in this paper, is extended over Y: = Y U {infinity} U {-infinity} 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. (C) 2015 Elsevier B.V. All rights reserved.