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

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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

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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

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  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. 

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