Cardinal functions $F_{\theta }(X)$ and $t_{\theta }(X)$ for H-closed spaces

Abstract

In this article, starting with results from a paper by Cammaroto and Kočinac in 1993, we prove that $t_{\theta }(X)=t_{\theta }(X_s)=t(X_s)=F_{\theta }(X)=F_{\theta }(X_s)=F(X_s)$ for every H-closed and Urysohn space and we present some useful examples to study the full relationships among the cardinal functions $t$, $t_{\theta }$, $F$ and $F_{\theta }$ in the context of H-closed and Urysohn spaces. Also, we construct an H-closed space $H$ for which $F_{\theta }(H)<t_{\theta }(H)$. Two questions posed by Cammaroto and Kočinac about H-closed spaces are answered.

This paper has been withdrawn by the author due to an error in chapter 4