Remarks on star countable discrete closed spaces

Yan-Kui Song

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 2, page 451-460
  • ISSN: 0011-4642

Abstract

top
In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) Assuming 2 ℵ 0 = 2 ℵ 1 , there exists a normal absolutely star countable discrete closed space having a regular-closed subspace which is not star countable.

How to cite

top

Song, Yan-Kui. "Remarks on star countable discrete closed spaces." Czechoslovak Mathematical Journal 63.2 (2013): 451-460. <http://eudml.org/doc/260594>.

@article{Song2013,
abstract = {In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) Assuming $2^\{\aleph _0\}=2^\{\aleph _1\}$, there exists a normal absolutely star countable discrete closed space having a regular-closed subspace which is not star countable.},
author = {Song, Yan-Kui},
journal = {Czechoslovak Mathematical Journal},
keywords = {pseudocompact; normal; Tychonoff; star countable; absolutely star countable; star countable discrete closed; absolutely star countable discrete closed space; pseudocompact; normal; Tychonoff; star countable; absolutely star countable; star countable discrete closed; absolutely star countable discrete closed space},
language = {eng},
number = {2},
pages = {451-460},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Remarks on star countable discrete closed spaces},
url = {http://eudml.org/doc/260594},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Song, Yan-Kui
TI - Remarks on star countable discrete closed spaces
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 2
SP - 451
EP - 460
AB - In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) Assuming $2^{\aleph _0}=2^{\aleph _1}$, there exists a normal absolutely star countable discrete closed space having a regular-closed subspace which is not star countable.
LA - eng
KW - pseudocompact; normal; Tychonoff; star countable; absolutely star countable; star countable discrete closed; absolutely star countable discrete closed space; pseudocompact; normal; Tychonoff; star countable; absolutely star countable; star countable discrete closed; absolutely star countable discrete closed space
UR - http://eudml.org/doc/260594
ER -

References

top
  1. Aiken, L. P., 10.1016/j.topol.2011.06.032, Topology Appl. 158 (2011), 1732-1737. (2011) Zbl1223.54029MR2812483DOI10.1016/j.topol.2011.06.032
  2. Alas, O. T., Junqueira, L. R., Wilson, R. G., 10.1016/j.topol.2010.12.012, Topology Appl. 158 (2011), 620-626. (2011) Zbl1226.54023MR2765618DOI10.1016/j.topol.2010.12.012
  3. Alas, O. T., Junqueira, L. R., Mill, J. van, Tkachuk, V. V., Wilson, R. G., 10.2478/s11533-011-0018-y, Cent. Eur. J. Math. 9 (2011), 603-615. (2011) MR2784032DOI10.2478/s11533-011-0018-y
  4. Bonanzinga, M., Star-Lindelöf and absolutely star-Lindelöf spaces, Questions Answers Gen. Topology. 16 (1998), 79-104. (1998) Zbl0931.54019MR1642032
  5. Engelking, R., General Topology. Rev. and compl. ed, Sigma Series in Pure Mathematics 6, Heldermann, Berlin (1989). (1989) Zbl0684.54001MR1039321
  6. Matveev, M. V., 10.1016/0166-8641(94)90074-4, Topology Appl. 58 (1994), 81-92. (1994) Zbl0801.54021MR1280711DOI10.1016/0166-8641(94)90074-4
  7. Matveev, M. V., A survey on star-covering properties, Topological Atlas preprint No 330 (1998). (1998) 
  8. Matveev, M. V., On space in countable web, arxiv:math/0006199v1 (2000). (2000) 
  9. Song, Y.-K., 10.21099/tkbjm/1496164294, Tsukuba J. Math. 25 (2001), 371-382. (2001) Zbl1011.54020MR1869769DOI10.21099/tkbjm/1496164294
  10. Song, Y.-K., Closed subsets of absolutely star-Lindelöf spaces II, Commentat. Math. Univ. Carol. 44 (2003), 329-334. (2003) Zbl1100.54017MR2026167
  11. Song, Y.-K., 10.1007/s10587-008-0053-4, Czech. Math. J. 58 (2008), 823-831. (2008) MR2455940DOI10.1007/s10587-008-0053-4
  12. Song, Y.-K., 10.1016/j.topol.2011.03.006, Topology Appl. 158 (2011), 1121-1123. (2011) Zbl1220.54008MR2794466DOI10.1016/j.topol.2011.03.006
  13. Tall, F. D., Normality versus collectionwise normality, Handbook of Set-Theoretic Topology K. Kunen and J. E. Vaughan North-Holland, Amsterdam (1984), 685-732. (1984) Zbl0552.54011MR0776634
  14. Douwen, E. K. van, Reed, G. M., Roscoe, A. W., Tree, I. J., 10.1016/0166-8641(91)90077-Y, Topology Appl. 39 (1991), 71-103. (1991) MR1103993DOI10.1016/0166-8641(91)90077-Y
  15. Mill, J. van, Tkachuk, V. V., Wilson, R. G., 10.1016/j.topol.2006.03.029, Topology Appl. 154 (2007), 2127-2134. (2007) MR2324924DOI10.1016/j.topol.2006.03.029
  16. Vaughan, J. E., 10.1111/j.1749-6632.1996.tb36814.x, Ann. N. Y. Acad. Sci. 788 (1996), 203-208. (1996) Zbl0917.54023MR1460834DOI10.1111/j.1749-6632.1996.tb36814.x
  17. Yasui, Y., Gao, Z.-M., Spaces in countable web, Houston J. Math. 25 (1999), 327-335. (1999) Zbl0974.54011MR1697629

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.