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

The research in this paper is a continuation of the investigation of the cardinality of the θ-closed hull of subsets of spaces. This research obtains new upper bounds of the cardinality of the θ-closed hull of subsets using cardinal functions of θ-bitightness ([8]), finite θ-bitightness ([7]) and θ-bitightness small number ([7]) of spaces. In the final section, examples of spaces are presented including one that answers a question posed in [4] and [6].