Uniform convergence structures in function spaces and preservation of continuity (Q1116483)

The authors show how a family of filters on X and an isotone uniform convergence structure \({\mathfrak A}\) on Y define an isotone uniform convergence structrure \({\mathfrak q}\) on \(Y^ X\) which generalizes most of the uniform convergence structures known in literature. \({\mathfrak q}\) is stable, (pseudo-, pre-) topological etc. if \({\mathfrak A}\) is. Further, for topological spaces X and locally quasi-uniform spaces Y they study the preservation of continuity in \({\mathfrak q}\) and the simple equicontinuity and compactness of families of functions.