# In search for Lindelöf ${C}_{p}$’s

Commentationes Mathematicae Universitatis Carolinae (2004)

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

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

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