Completeness properties of the generalized compact-open topology on partial functions with closed domains

The primary goal of the paper is to investigate the Baire property and weak alpha -favorability for the generalized compact-open topology tau (C) on the space P of continuous partial functions f : A --> Y with a closed domain A subset of X. Various sufficient and necessary conditions are given. It is shown, e.g,, that (P, tau (C)) is weakly alpha -favorable (and hence a Baire space), if X is a locally compact paracompact space and Y is a regular space having a completely metrizable dense subspace. As corollaries we get sufficient conditions for Baireness and weak alpha -favorability of the graph topology of Brandi and Ceppitelli introduced for applications in differential equations, as well as of the Fell hyperspace topology. The relationship between tau (C), the compact-open and Fell topologies, respectively is studied; moreover, a topological game is introduced and studied in order to facilitate the exposition of the above results. (C) 2001 Elsevier Science B.V. All rights reserved.