Geodesic
$\omega$H-sets and cardinal invariants
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 2, pp. 367-370.

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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 $X$.
Classification : 54A25, 54D20
Keywords: cardinal function; $\omega$H-set 
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     author = {Fedeli, Alessandro},
     title = {$\omega${H-sets} and cardinal invariants},
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Fedeli, Alessandro. $\omega$H-sets and cardinal invariants. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 2, pp. 367-370. http://geodesic.mathdoc.fr/item/CMUC_1998__39_2_a12/