Abstract:A subset $A$ of a Hausdorff space $X$ is called an $\omega $H-set in $X$ if for every open family $\Cal U$ in $X$ such that $A \subset \bigcup \Cal U$ there exists a countable subfamily $\Cal V$ of $\Cal U$ such that $A \subset \bigcup \{ \overline {V} : V \in \Cal V \}$. In this paper we introduce a new cardinal function $t_{s\theta }$ and show that $|A| \leq 2^{t_{s\theta }(X)\psi _{c}(X)}$ for every $\omega $H-set $A$ of a Hausdorff space $X$.
Keywords: cardinal function, $\omega $H-set
AMS Subject Classification: 54A25, 54D20