Generalized Frol\'ik classes

TL;DR

This paper generalizes Frolík classes to broader topological properties defined via filter convergence, providing characterizations applicable to many classes of spaces.

Contribution

It introduces a unified framework for generalized Frolík classes based on filter convergence, extending previous classes related to countable compactness and pseudocompactness.

Findings

Characterization of generalized Frolík classes for properties defined by filter convergence

Extension of Frolík classes to broader topological properties

Applicable to classes of spaces defined via filter convergence

Abstract

The class $\mathfrak C $ relative to countably compact topological spaces and the class $\mathfrak P$ relative to pseudocompact spaces introduced by Z. Frol\'ik are naturally generalized relative to every topological property. We provide a characterization of such generalized Frol\'ik 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 Frol\'ik class.