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Keywords:
convergence space; cardinal function; inequality; set-theoretic topology
convergence space; cardinal function; inequality; set-theoretic topology
Summary:
We extend the Noble and Ulmer theorem and the Juhász and Hajnal theorems in set-theoretic topology. We show that a statement analogous to that in the former theorem is valid for a family of almost topological convergences, whereas statements analogous to those in the latter theorems hold for a pretopologically Hausdorff convergence.
References:
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