Mathematica Bohemica, Vol. 146, No. 2, pp. 215-227, 2021
Remarks on cardinal inequalities in convergence spaces
Kazushi Yoshitomi
Received June 19, 2019. Published online August 20, 2020.
Abstract: 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.
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Affiliations: Kazushi Yoshitomi, Department of Mathematical Sciences, Tokyo Metropolitan University, Minamiohsawa 1-1, Hachioji, Tokyo 192-0397, Japan, e-mail: yositomi@tmu.ac.jp
