On the cardinality of the $θ$-closed hull of sets II

Filippo Cammaroto, Andrei Catalioto, Bruno Antonio Pansera, Jack Porter

Published 2012-06-28, updated 2012-12-17Version 2

The research in this paper is a continuation of the investigation of the cardinality of the $\theta$-closed hull of subsets of spaces. This research obtains new upper bounds of the cardinality of the $\theta$-closed hull of subsets using cardinal functions of $\theta$-bitightness (\cite{Ca-Ko}), finite $\theta$-bitightness (\cite{Ca-Ca-Pa-Ts}) and $\theta$-bitightness small number (\cite{Ca-Ca-Pa-Ts}) of spaces. In the final section, examples of spaces are presented including one that answers a question posed in \cite{Bo-Ca-Ma} and \cite{Bo-Pa}.