A method of returning vector-valued maps to real-valued functions on monotone operators

Let Y be an ordered topological vector space with a positive interior point e. Motivated by the Minkowski functional p(e), we introduce the function q(e) on the interior int(Y) Y+ of the positive cone of Y. The function q(e) plays a role for evaluating a 'reverse gauge' of the Minkowski functional p(e) on the restricted space int(Y) Y+. We also apply the function q(e) for giving complete proof of the recent results [7] by Jin, Xie and Yue on monotonically countably paracompact spaces. New characterizations by vector-valued continuous maps are also given for stratifiable spaces and monotone cb-spaces, the latter provides a positive answer to a question posed in [12] by the author. (C) 2018 Elsevier B.V. All rights reserved.