Some compactness properties related to pseudocompactness and ultrafilter convergence

Paolo Lipparini

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arXiv · 0907.0602

Some compactness properties related to pseudocompactness and ultrafilter convergence

Paolo Lipparini

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Abstract

We discuss some notions of compactness and convergence relative to a specified family F of subsets of some topological space X. The two most interesting particular cases of our construction appear to be the following ones. (1) The case in which F is the family of all singletons of X, in which case we get back the more usual notions. (2) The case in which F is the family of all nonempty open subsets of X, in which case we get notions related to pseudocompactness. A large part of the results in this note are known in particular case (1); the results are, in general, new in case (2). As an example, we characterize those spaces which are D-pseudocompact, for some ultrafilter D uniform over $λ$.

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Paolo Lipparini. 2010-01-22. Some compactness properties related to pseudocompactness and ultrafilter convergence. https://arxiv.org/abs/0907.0602

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