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

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

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