$\omega$H-sets and cardinal invariants

Fedeli, Alessandro

Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998), p. 367-370 / Harvested from Czech Digital Mathematics Library

Résumé

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 $X$.

Détail

Publié le : 1998-01-01

MR 1651975 | Zbl 0937.54004

Classification:  54A25,  54D20

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