On the cardinality of functionally Hausdorff spaces

Alessandro Fedeli

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 4, page 797-801
  • ISSN: 0010-2628

Abstract

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In this paper two new cardinal functions are introduced and investigated. In particular the following two theorems are proved: (i) If X is a functionally Hausdorff space then | X | ≤ 2 f s ( X ) ψ τ ( X ) ; (ii) Let X be a functionally Hausdorff space with f s ( X ) ≤ κ . Then there is a subset S of X such that | S | ≤ 2 κ and X = ⋃ { c l τ θ ( A ) : A ∈ [ S ] ≤ κ } .

How to cite

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Fedeli, Alessandro. "On the cardinality of functionally Hausdorff spaces." Commentationes Mathematicae Universitatis Carolinae 37.4 (1996): 797-801. <http://eudml.org/doc/247911>.

@article{Fedeli1996,
abstract = {In this paper two new cardinal functions are introduced and investigated. In particular the following two theorems are proved: (i) If $\,X$ is a functionally Hausdorff space then $|X| \le 2^\{fs(X) \psi _\{\tau \}(X)\}$; (ii) Let $X$ be a functionally Hausdorff space with $fs(X) \le \kappa $. Then there is a subset $S$ of $X$ such that $|S| \le 2^\{\kappa \}$ and $X = \bigcup \lbrace cl_\{\tau \theta \}(A): A \in [S]^\{\le \kappa \} \rbrace $.},
author = {Fedeli, Alessandro},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {cardinal functions; $\tau $-pseudocharacter; functional spread; -pseudocharacter; functional spread; cardinal characteristics of a topological space},
language = {eng},
number = {4},
pages = {797-801},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the cardinality of functionally Hausdorff spaces},
url = {http://eudml.org/doc/247911},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Fedeli, Alessandro
TI - On the cardinality of functionally Hausdorff spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 4
SP - 797
EP - 801
AB - In this paper two new cardinal functions are introduced and investigated. In particular the following two theorems are proved: (i) If $\,X$ is a functionally Hausdorff space then $|X| \le 2^{fs(X) \psi _{\tau }(X)}$; (ii) Let $X$ be a functionally Hausdorff space with $fs(X) \le \kappa $. Then there is a subset $S$ of $X$ such that $|S| \le 2^{\kappa }$ and $X = \bigcup \lbrace cl_{\tau \theta }(A): A \in [S]^{\le \kappa } \rbrace $.
LA - eng
KW - cardinal functions; $\tau $-pseudocharacter; functional spread; -pseudocharacter; functional spread; cardinal characteristics of a topological space
UR - http://eudml.org/doc/247911
ER -

References

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  10. Schröder J., Urysohn cellularity and Urysohn spread, Math. Japonicae 38 (1993), 1129-1133. (1993) MR1250339
  11. Shapirovskii B., On discrete subspaces of topological spaces. Weight, tightness and Suslin number, Soviet Math. Dokl. 13 (1972), 215-219. (1972) 
  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. (1990) Zbl0717.54002MR1077911
  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. Zbl0803.54001MR1229141
  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. (1994) Zbl0836.54004MR1280708

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