On the cardinality of functionally Hausdorff spaces
Fedeli, Alessandro
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996), p. 797-801 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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 $X = \bigcup \{ cl_{\tau \theta}(A): A \in [S]^{\leq \kappa} \}$.

Publié le : 1996-01-01
Classification:  54A25,  54D10,  54D70 
@article{118886,
     author = {Alessandro Fedeli},
     title = {On the cardinality of functionally Hausdorff spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {37},
     year = {1996},
     pages = {797-801},
     zbl = {0886.54004},
     mrnumber = {1440709},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118886}
}

Fedeli, Alessandro. On the cardinality of functionally Hausdorff spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 797-801. http://gdmltest.u-ga.fr/item/118886/

Engelking R. General Topology. Revised and completed edition, Sigma Series in Pure Mathematics 6, Heldermann Verlag, Berlin (1989). (1989) | MR 1039321

Fedeli A. Two cardinal inequalities for functionally Hausdorff spaces, Comment. Math. Univ. Carolinae 35.2 (1994), 365-369. (1994) | MR 1286584 | Zbl 0807.54006

Fedeli A.; Watson S. Elementary Submodels in Topology, submitted.

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

Ishii T. On the Tychonoff functor and w-compactness, Topology Appl. 11 (1980), 175-187. (1980) | MR 0572372 | Zbl 0441.54012

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

Juhàsz I. Cardinal functions in topology-ten years later, Mathematical Centre Tracts 123, Amsterdam, 1980. | MR 0576927

Kočinac Lj. Some cardinal functions on Urysohn spaces, to appear. | MR 1385570

Kočinac Lj. On the cardinality of Urysohn and $H$-closed spaces, Proc. of the Mathematical Conference in Priština, 1994, pp. 105-111. | MR 1466279

Schröder J. Urysohn cellularity and Urysohn spread, Math. Japonicae 38 (1993), 1129-1133. (1993) | MR 1250339

Shapirovskii B. On discrete subspaces of topological spaces. Weight, tightness and Suslin number, Soviet Math. Dokl. 13 (1972), 215-219. (1972)

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. (1990) | MR 1077911 | Zbl 0717.54002

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

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. (1994) | MR 1280708 | Zbl 0836.54004