Generalized Frolík classes

Abstract

The class $\mathfrak{C}$ relative to countably compact topological spaces and the class $\mathfrak{P}$ relative to pseudocompact spaces introduced by Z. Frolík are naturally generalized relative to every topological property. We provide a characterization of such generalized Frolík classes in the broad case of properties defined in terms of filter convergence. If a class of spaces can be defined in terms of filter convergence, then the same is true for its Frolík class.

8 pages