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Generalized Frolík classes

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.