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

top
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

top

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

top
  1. Engelking R., General Topology. Revised and completed edition, Sigma Series in Pure Mathematics 6, Heldermann Verlag, Berlin (1989). (1989) MR1039321
  2. Fedeli A., Two cardinal inequalities for functionally Hausdorff spaces, Comment. Math. Univ. Carolinae 35.2 (1994), 365-369. (1994) Zbl0807.54006MR1286584
  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. Zbl0559.54003MR0776620
  5. Ishii T., On the Tychonoff functor and w-compactness, Topology Appl. 11 (1980), 175-187. (1980) Zbl0441.54012MR0572372
  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. Zbl0763.54009MR1053197
  7. Juhàsz I., Cardinal functions in topology-ten years later, Mathematical Centre Tracts 123, Amsterdam, 1980. MR0576927
  8. Kočinac Lj., Some cardinal functions on Urysohn spaces, to appear. MR1385570
  9. Kočinac Lj., On the cardinality of Urysohn and H -closed spaces, Proc. of the Mathematical Conference in Priština, 1994, pp. 105-111. MR1466279
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.