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Keywords:
cardinal functions; $\tau$-pseudocharacter; functional spread
cardinal functions; $\tau$-pseudocharacter; functional spread
Summary:
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 $X = \bigcup \{ cl_{\tau \theta}(A): A \in [S]^{\leq \kappa} \}$.
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