Cardinal functions $F_θ(X)$ and $t_θ(X)$ for H-closed spaces

Filippo Cammaroto, Andrei Catalioto, Jack Porter

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

In this article, starting with results from a paper by Cammaroto and Ko\v{c}inac 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 Ko\v{c}inac about H-closed spaces are answered.