The Baire property in the compact-open topology of Lasnev spaces

Finding an internal condition on a topological space X which is necessary and sufficient for the compact-open topology C-k(X) to be Baire is an open problem. The moving off property is a known characterization for the class of first-countable or locally compact spaces. Here we show that it also holds for the class of closed images of first-countable paracompact spaces, hence Lagnev spaces in particular; furthermore, Baireness of C-k (X) is equivalent to its alpha-favorability for X in this class. We will also show that if X is the closed image of a locally compact paracompact space then C-k (X) is alpha-favorable. (C) 2016 Elsevier B.V. All rights reserved.