In search for Lindelöf C p ’s

Raushan Z. Buzyakova

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 1, page 145-151
  • ISSN: 0010-2628

Abstract

top
It is shown that if X is a first-countable countably compact subspace of ordinals then C p ( X ) is Lindelöf. This result is used to construct an example of a countably compact space X such that the extent of C p ( X ) is less than the Lindelöf number of C p ( X ) . This example answers negatively Reznichenko’s question whether Baturov’s theorem holds for countably compact spaces.

How to cite

top

Buzyakova, Raushan Z.. "In search for Lindelöf $C_p$’s." Commentationes Mathematicae Universitatis Carolinae 45.1 (2004): 145-151. <http://eudml.org/doc/249359>.

@article{Buzyakova2004,
abstract = {It is shown that if $X$ is a first-countable countably compact subspace of ordinals then $C_p(X)$ is Lindelöf. This result is used to construct an example of a countably compact space $X$ such that the extent of $C_p(X)$ is less than the Lindelöf number of $C_p(X)$. This example answers negatively Reznichenko’s question whether Baturov’s theorem holds for countably compact spaces.},
author = {Buzyakova, Raushan Z.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$C_p(X)$; space of ordinals; Lindelöf space; ; space of ordinals; Lindelöf space; countably compact space},
language = {eng},
number = {1},
pages = {145-151},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {In search for Lindelöf $C_p$’s},
url = {http://eudml.org/doc/249359},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Buzyakova, Raushan Z.
TI - In search for Lindelöf $C_p$’s
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 1
SP - 145
EP - 151
AB - It is shown that if $X$ is a first-countable countably compact subspace of ordinals then $C_p(X)$ is Lindelöf. This result is used to construct an example of a countably compact space $X$ such that the extent of $C_p(X)$ is less than the Lindelöf number of $C_p(X)$. This example answers negatively Reznichenko’s question whether Baturov’s theorem holds for countably compact spaces.
LA - eng
KW - $C_p(X)$; space of ordinals; Lindelöf space; ; space of ordinals; Lindelöf space; countably compact space
UR - http://eudml.org/doc/249359
ER -

References

top
  1. Arhangelskii A., Topological Function Spaces, Math. Appl., vol. 78, Kluwer Academic Publisher, Dordrecht, 1992. MR1144519
  2. Asanov M.O., On cardinal invariants of function spaces, Modern Topology and Set Theory, Igevsk, (2), 1979, 8-12. 
  3. Baturov D., On subspaces of function spaces, Vestnik MGU, Mat. Mech. 4 (1987), 66-69. (1987) Zbl0665.54004MR0913076
  4. Buzyakova R., Hereditary D-property of Function Spaces Over Compacta, submitted to Proc. Amer. Math. Soc. Zbl1064.54029MR2073321
  5. van Douwen E.K., Simultaneous extension of continuous functions, Thesis, Free University, Amsterdam, 1975. 
  6. Engelking R., General Topology, Sigma Series in Pure Mathematics, 6, Heldermann, Berlin, revised ed., 1989. Zbl0684.54001MR1039321
  7. Nahmanson L.B., Lindelöfness in function spaces, Fifth Teraspol Symposium on Topology and its Applications, Kishinev, 1985, p.183. 

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.