Completeness Properties in Function Spaces with the Compact-Open Topology

Abstract

It is an open problem to characterize those spaces X for which the compact-open topology C_k(X) has various completeness properties. It is conjectured that C_k(X) is Baire if and only if X has the moving off property. We show this conjecture is true for special classes of spaces: fans, closed images of first countable paracompact spaces, Lasnev Spaces, and certain types of collapsed spaces. We also introduce a new completeness properties motivated by the Cech complete property.