Geodesic
On the cardinality of functionally Hausdorff spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 4, pp. 797-801

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In this paper two new cardinal functions are introduced and investigated. In particular the following two theorems are proved: \noindent {\rm (i)} If $\,X$ is a functionally Hausdorff space then $|X| \leq 2^{fs(X) \psi_{\tau}(X)}$; \noindent {\rm (ii)} Let $X$ be a functionally Hausdorff space with $fs(X) \leq \kappa$. Then there is a subset $S$ of $X$ such that $|S| \leq 2^{\kappa}$ and $X = \bigcup \{ cl_{\tau \theta}(A): A \in [S]^{\leq \kappa} \}$.
In this paper two new cardinal functions are introduced and investigated. In particular the following two theorems are proved: \noindent {\rm (i)} If $\,X$ is a functionally Hausdorff space then $|X| \leq 2^{fs(X) \psi_{\tau}(X)}$; \noindent {\rm (ii)} Let $X$ be a functionally Hausdorff space with $fs(X) \leq \kappa$. Then there is a subset $S$ of $X$ such that $|S| \leq 2^{\kappa}$ and $X = \bigcup \{ cl_{\tau \theta}(A): A \in [S]^{\leq \kappa} \}$.
Classification : 54A25, 54D10, 54D70
Keywords: cardinal functions; $\tau$-pseudocharacter; functional spread 
Fedeli, Alessandro. On the cardinality of functionally Hausdorff spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) no. 4, pp. 797-801. http://geodesic.mathdoc.fr/item/CMUC_1996_37_4_a10/
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     author = {Fedeli, Alessandro},
     title = {On the cardinality of functionally {Hausdorff} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {797--801},
     year = {1996},
     volume = {37},
     number = {4},
     mrnumber = {1440709},
     zbl = {0886.54004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1996_37_4_a10/}
}
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