Note on countable unions of Corson countably compact spaces

Ondřej F. K. Kalenda

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 3, page 499-507
  • ISSN: 0010-2628

Abstract

top
We show that a compact space K has a dense set of G δ points if it can be covered by countably many Corson countably compact spaces. If these Corson countably compact spaces may be chosen to be dense in K , then K is even Corson.

How to cite

top

Kalenda, Ondřej F. K.. "Note on countable unions of Corson countably compact spaces." Commentationes Mathematicae Universitatis Carolinae 45.3 (2004): 499-507. <http://eudml.org/doc/249382>.

@article{Kalenda2004,
abstract = {We show that a compact space $K$ has a dense set of $G_\delta $ points if it can be covered by countably many Corson countably compact spaces. If these Corson countably compact spaces may be chosen to be dense in $K$, then $K$ is even Corson.},
author = {Kalenda, Ondřej F. K.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Corson countably compact space; $G_\delta $ point; Corson compact space; Valdivia compact space; Corson countably compact space; point; Corson compact space; Valdivia compact space},
language = {eng},
number = {3},
pages = {499-507},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Note on countable unions of Corson countably compact spaces},
url = {http://eudml.org/doc/249382},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Kalenda, Ondřej F. K.
TI - Note on countable unions of Corson countably compact spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 3
SP - 499
EP - 507
AB - We show that a compact space $K$ has a dense set of $G_\delta $ points if it can be covered by countably many Corson countably compact spaces. If these Corson countably compact spaces may be chosen to be dense in $K$, then $K$ is even Corson.
LA - eng
KW - Corson countably compact space; $G_\delta $ point; Corson compact space; Valdivia compact space; Corson countably compact space; point; Corson compact space; Valdivia compact space
UR - http://eudml.org/doc/249382
ER -

References

top
  1. Argyros S., Mercourakis S., On weakly Lindelöf Banach spaces, Rocky Mountain J. Math. 23 (1993), 395-446. (1993) Zbl0797.46009MR1226181
  2. Argyros S., Mercourakis S., Negrepontis S., Functional analytic properties of Corson compact spaces, Studia Math. 89 (1988), 197-229. (1988) Zbl0656.46014MR0956239
  3. Gul'ko S.P., Properties of sets that lie in Σ -products (in Russian), Dokl. Akad. Nauk SSSR 237 (1977), 3 505-508. (1977) MR0461410
  4. Kalenda O., Continuous images and other topological properties of Valdivia compacta, Fund Math. 162 (1999), 2 181-192. (1999) Zbl0989.54019MR1734916
  5. Kalenda O., A characterization of Valdivia compact spaces, Collectanea Math. 51 1 (2000), 59-81. (2000) Zbl0949.46004MR1757850
  6. Kalenda O., Embedding of the ordinal segment [ 0 , ø m e g a 1 ] into continuous images of Valdivia compacta, Comment. Math. Univ. Carolinae 40 4 (1999), 777-783. (1999) Zbl1009.54017MR1756552
  7. Kalenda O., Valdivia compact spaces in topology and Banach space theory, Extracta Math. 15 1 (2000), 1-85. (2000) Zbl0983.46021MR1792980
  8. Kalenda O., On the class of continuous images of Valdivia compacta, Extracta Math. 18 (2003), 1 65-80. (2003) Zbl1159.46306MR1989298
  9. Kubiś W., Uspenskij V., A compact group which is not Valdivia compact, Proc. Amer. Math. Soc., to appear. MR2138892
  10. Michael E., Rudin M.E., A note on Eberlein compacts, Pacific J. Math. 72 (1977), 2 487-495. (1977) Zbl0345.54020MR0478092
  11. Noble N., The continuity of functions on Cartesian products, Trans. Amer. Math. Soc. 149 (1970), 187-198. (1970) Zbl0229.54028MR0257987
  12. Orihuela J., On Weakly Lindelöf Banach spaces, Progress in Funct. Anal. K.D. Bierstedt, J. Bonet, J. Horváth, M. Maestre Elsevier Sci. Publ. B.V. (1992), 279-291. (1992) MR1150753
  13. Sokolov G.A., On some classes of compact spaces lying in Σ -products, Comment. Math. Univ. Carolinae 25 (1984), 219-231. (1984) Zbl0577.54014MR0768809
  14. Valdivia M., Resolutions of the identity in certain Banach spaces, Collectanea Math. 39 (1988), 2 127-140. (1988) Zbl0718.46006MR1027683
  15. Valdivia M., On certain compact topological spaces, Rev. Mat. Univ. Complut. Madrid 10 1 (1997), 81-84. (1997) Zbl0870.54025MR1452564

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.