Previous |  Up |  Next


cardinal functions; $\tau$-pseudocharacter; functional spread
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 $X = \bigcup \{ cl_{\tau \theta}(A): A \in [S]^{\leq \kappa} \}$.
[1] Engelking R.: General Topology. Revised and completed edition. Sigma Series in Pure Mathematics 6, Heldermann Verlag, Berlin (1989). MR 1039321
[2] Fedeli A.: Two cardinal inequalities for functionally Hausdorff spaces. Comment. Math. Univ. Carolinae 35.2 (1994), 365-369. MR 1286584 | Zbl 0807.54006
[3] Fedeli A., Watson S.: Elementary Submodels in Topology. submitted.
[4] Hodel R.: Cardinal Functions I. Handbook of Set-theoretic Topology, (Kunen K. and Vaughan J.E., eds.) Elsevier Science Publishers, B.V., North Holland, 1984, pp. 1-61. MR 0776620 | Zbl 0559.54003
[5] Ishii T.: On the Tychonoff functor and w-compactness. Topology Appl. 11 (1980), 175-187. MR 0572372 | Zbl 0441.54012
[6] Ishii T.: The Tychonoff functor and related topics. Topics in General Topology, (Morita K. and Nagata J., eds.) Elsevier Science Publishers, B.V., North Holland, 1989, pp. 203-243. MR 1053197 | Zbl 0763.54009
[7] Juhàsz I.: Cardinal functions in topology-ten years later. Mathematical Centre Tracts 123, Amsterdam, 1980. MR 0576927
[8] Kočinac Lj.: Some cardinal functions on Urysohn spaces. to appear. MR 1385570
[9] Kočinac Lj.: On the cardinality of Urysohn and $H$-closed spaces. Proc. of the Mathematical Conference in Priština, 1994, pp. 105-111. MR 1466279
[10] Schröder J.: Urysohn cellularity and Urysohn spread. Math. Japonicae 38 (1993), 1129-1133. MR 1250339
[11] Shapirovskii B.: On discrete subspaces of topological spaces. Weight, tightness and Suslin number. Soviet Math. Dokl. 13 (1972), 215-219.
[12] Sun S.H., Choo K.G.: Some new cardinal inequalities involving a cardinal function less than the spread and the density. Comment. Math. Univ. Carolinae 31.2 (1990), 395-401. MR 1077911 | Zbl 0717.54002
[13] Watson S.: The construction of topological spaces: Planks and Resolutions. Recent Progress in General Topology, (Hušek M. and Van Mill J., eds.) Elsevier Science Publishers, B.V., North Holland, 1992, pp. 675-757. MR 1229141 | Zbl 0803.54001
[14] Watson S.: The Lindelöf number of a power: an introduction to the use of elementary submodels in general topology. Topology Appl. 58 (1994), 25-34. MR 1280708 | Zbl 0836.54004
Partner of
EuDML logo