A note on discrete sets

Santi Spadaro

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 3, page 463-475
  • ISSN: 0010-2628

Abstract

top
We give several partial positive answers to a question of Juhász and Szentmiklóssy regarding the minimum number of discrete sets required to cover a compact space. We study the relationship between the size of discrete sets, free sequences and their closures with the cardinality of a Hausdorff space, improving known results in the literature.

How to cite

top

Spadaro, Santi. "A note on discrete sets." Commentationes Mathematicae Universitatis Carolinae 50.3 (2009): 463-475. <http://eudml.org/doc/33328>.

@article{Spadaro2009,
abstract = {We give several partial positive answers to a question of Juhász and Szentmiklóssy regarding the minimum number of discrete sets required to cover a compact space. We study the relationship between the size of discrete sets, free sequences and their closures with the cardinality of a Hausdorff space, improving known results in the literature.},
author = {Spadaro, Santi},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {discrete set; dispersion character; compact space; Eberlein compact; free sequence; elementary submodel; discrete set; dispersion character; compact space; Eberlein compact; free sequence; elementary submodel},
language = {eng},
number = {3},
pages = {463-475},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on discrete sets},
url = {http://eudml.org/doc/33328},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Spadaro, Santi
TI - A note on discrete sets
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 3
SP - 463
EP - 475
AB - We give several partial positive answers to a question of Juhász and Szentmiklóssy regarding the minimum number of discrete sets required to cover a compact space. We study the relationship between the size of discrete sets, free sequences and their closures with the cardinality of a Hausdorff space, improving known results in the literature.
LA - eng
KW - discrete set; dispersion character; compact space; Eberlein compact; free sequence; elementary submodel; discrete set; dispersion character; compact space; Eberlein compact; free sequence; elementary submodel
UR - http://eudml.org/doc/33328
ER -

References

top
  1. Alas O., On closures of discrete subsets, Questions Answers Gen. Topology 20 (2002), 85--89. Zbl1017.54003MR1910436
  2. Alas O., Tkachuk V., Wilson R., Closures of discrete sets often reflect global properties, Topology Proc. 25 (2000), Spring, 27--44. Zbl1002.54021MR1875581
  3. Arhangel'skii A.V., 10.1070/RM1978v033n06ABEH003884, Russian Math. Surveys 33 (1978), 33--96. MR0526012DOI10.1070/RM1978v033n06ABEH003884
  4. Dow A., An introduction to applications of elementary submodels to topology, Topology Proc. 13 (1988), no. 1, 17--72. Zbl0696.03024MR1031969
  5. Dow A., Closures of discrete sets in compact spaces, Studia Math. Sci. Hung. 42 (2005), 227--234. Zbl1081.54004MR2146153
  6. Engelking R., General Topology, second ed., Sigma Series in Pure Mathematics, no. 6, Heldermann Verlag, Berlin, 1989. Zbl0684.54001MR1039321
  7. Gerlits J., 10.1007/BF02018038, Period. Math. Hungar. 4 (1973), 71--80. Zbl0275.54005MR0339076DOI10.1007/BF02018038
  8. Gerlits J., On a generalization of dyadicity, Studia Sci. Math. Hungar. 13 (1978), 1--17. Zbl0475.54012MR0630375
  9. Gerlits J., Juhász I., Szentmiklóssy Z., Two improvements on Tkachenko's addition theorem, Comment. Math. Univ. Carolin., 46 (2005), no. 4, 705--710. MR2259500
  10. Gruenhage G., Generalized metric spaces, in Handbook of Set Theoretic Topology, K. Kunen and J.E. Vaughan, Eds., North-Holland, Amsterdam, 1984. Zbl0794.54034MR0776629
  11. Gruenhage G., A note on Gul'ko compact spaces, Proc. Amer. Math. Soc. 100 (1987), 371--376. Zbl0622.54020MR0884482
  12. Gruenhage G., Covering compacta by discrete and other separated sets, preprint. MR2502010
  13. Juhász I., Cardinal Function in Topology - Ten Years Later, Mathematical Centre Tracts, 123, Mathematisch Centrum, Amsterdam, 1980. MR0576927
  14. Juhász I., van Mill J., 10.1016/j.topol.2006.04.012, Topology Appl. 154 (2007), 283--286. MR2278676DOI10.1016/j.topol.2006.04.012
  15. I. Juhász, Z. Szentmiklóssy, A strengthening of the Čech-Pospišil theorem, preprint. MR2457995
  16. Leiderman A., Sokolov G., Adequate families of sets and Corson compacts, Comment. Math. Univ. Carolin. 25 (1984), no. 2, 233--246. Zbl0586.54022MR0768810
  17. Ridderbos G.J., Power homogeneity in topology, Doctoral Thesis, Vrije Universiteit, Amsterdam, 2007. 
  18. Spadaro S., 10.1016/j.topol.2008.09.009, Topology Appl. 156 (2009), 721--727. Zbl1161.54001MR2492957DOI10.1016/j.topol.2008.09.009
  19. Watson S., 10.4153/CJM-1982-078-8, Canad. J. Math., vol. XXXIV, no. 5, 1982, 1091--1096. Zbl0502.54016MR0675681DOI10.4153/CJM-1982-078-8
  20. Yakovlev N., On bicompacta in Σ -products and related spaces, Comment. Math. Univ. Carolin. 21 (1980), no. 2, 263--283. Zbl0436.54019MR0580682

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.