Closed subsets of absolutely star-Lindelöf spaces II

Yan-Kui Song

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 2, page 329-334
  • ISSN: 0010-2628

Abstract

top
In this paper, we prove the following two statements: (1) There exists a discretely absolutely star-Lindelöf Tychonoff space having a regular-closed subspace which is not CCC-Lindelöf. (2) Every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented in a Hausdorff (regular, Tychonoff) absolutely star-Lindelöf space as a closed G δ subspace.

How to cite

top

Song, Yan-Kui. "Closed subsets of absolutely star-Lindelöf spaces II." Commentationes Mathematicae Universitatis Carolinae 44.2 (2003): 329-334. <http://eudml.org/doc/249182>.

@article{Song2003,
abstract = {In this paper, we prove the following two statements: (1) There exists a discretely absolutely star-Lindelöf Tychonoff space having a regular-closed subspace which is not CCC-Lindelöf. (2) Every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented in a Hausdorff (regular, Tychonoff) absolutely star-Lindelöf space as a closed $G_\{\delta \}$ subspace.},
author = {Song, Yan-Kui},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {star-Lindelöf space; absolutely star-Lindelöf space; discretely absolutely star-Lindelöf space; CCC-Lindelöf space; star-Lindelöf space},
language = {eng},
number = {2},
pages = {329-334},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Closed subsets of absolutely star-Lindelöf spaces II},
url = {http://eudml.org/doc/249182},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Song, Yan-Kui
TI - Closed subsets of absolutely star-Lindelöf spaces II
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 2
SP - 329
EP - 334
AB - In this paper, we prove the following two statements: (1) There exists a discretely absolutely star-Lindelöf Tychonoff space having a regular-closed subspace which is not CCC-Lindelöf. (2) Every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented in a Hausdorff (regular, Tychonoff) absolutely star-Lindelöf space as a closed $G_{\delta }$ subspace.
LA - eng
KW - star-Lindelöf space; absolutely star-Lindelöf space; discretely absolutely star-Lindelöf space; CCC-Lindelöf space; star-Lindelöf space
UR - http://eudml.org/doc/249182
ER -

References

top
  1. Bonanzinga M., Star-Lindelöf and absolutely star-Lindelöf spaces, Questions Answers Gen. Topology 16 (1998), 79-104. (1998) Zbl0931.54019MR1642032
  2. Bonanzinga M., Matveev M.V., Closed subspaces of star-Lindelöf and related spaces, to appear in East-West J. Math. Zbl0997.54035MR1825453
  3. Bonanzinga M., Matveev M.V., Products of star-Lindelöf and related spaces, Houston J. Math. 27 (2001), 45-57. (2001) Zbl0983.54006MR1843911
  4. van Douwen E.K., Reed G.M., Roscoe A.W., Tree I.J., 10.1016/0166-8641(91)90077-Y, Topology Appl. 39 (1991), 71-103. (1991) Zbl0743.54007MR1103993DOI10.1016/0166-8641(91)90077-Y
  5. Engelking R., General Topology, Revised and completed edition, Heldermann Verlag Berlin (1989). (1989) MR1039321
  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, Topology Atlas preprint No. 330 (1998). 
  8. Song Y.-K., Remarks on star-Lindelöf spaces, Questions Answers Gen. Topology 20 (2002), 49-51. (2002) Zbl1006.54032MR1910431
  9. Song Y.-K., Shi W.-X., Closed subspaces of absolutely star-Lindelöf spaces, to appear in Houston J. Math. MR2084912
  10. Vaughan J.E., 10.1111/j.1749-6632.1996.tb36814.x, Annals of the New York Acad. Sci. 788 (1996), 203-208. (1996) Zbl0917.54023MR1460834DOI10.1111/j.1749-6632.1996.tb36814.x
  11. Vaughan J.E., Absolute countable compactness and property ( a ) , Talk at 1996 Praha symposium on General Topology. 

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.