
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 relative to countably compact topological spaces and the class 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.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Approximation Theory and Sequence Spaces
