Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Hereditary D-property of function spaces over compacta

Author(s): Raushan Z. Buzyakova
Journal: Proc. Amer. Math. Soc. 132 (2004), 3433-3439.
MSC (2000): Primary 54C35, 54D20, 54C60
Posted: May 20, 2004
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: It is shown that if $X$ is compact then every subspace of $C_p(X)$ is a $D$-space in the sense of E. van Douwen, which positively answers Matveev's question. A connection between the $D$-property and Baturov's and Grothendieck's classical theorems about function spaces over compacta is established.

References:

[ARH]
A. Arhangelskii, Topological function spaces, Math. Appl., vol. 78, Kluwer Academic Publisher, Dordrecht, 1992. MR 92i:54022

[A&B]
A. Arhangelskii and R. Buzyakova, Addition theorems and $D$-spaces, Comment. Math. Universitatis Carolinae 43, 4(2002), 653-663.

[BAT]
D. Baturov, On subspaces of function spaces, Vestn. Moskov. Univ. Ser. I Mat. Mech., 1987, no. 4, 66-69; English transl. in Moscow Univ. Math. Bull. 52 (1997). MR 89a:54018

[BUZ]
R. Buzyakova, On $D$-property of strong $\Sigma $-spaces., Comment. Math. Universitatis Carolinae, 43, 3(2002), 493-495. MR 2003j:54021

[B&W1]
C.R. Borges and A.C. Wehrly, A study of $D$-spaces. Topology Proc. 16 (1991), 7 - 15. MR 94a:54059

[B&W2]
C.R. Borges and A.C. Wehrly, Another study of $D$-spaces. Questions and Answers in General Topology 14:1 (1996), 73 - 76. MR 96m:54033

[B&W3]
C.R. Borges and A.C. Wehrly, Correction: another study of $D$-spaces. Questions and Answers in General Topology 16:1 (1998), 77 - 78. MR 98m:54026

[DCA]
P. DeCaux, Yet another property of the Sorgenfrey plane, Topology Proc. 6:1 (1981), 31-43. MR 83h:54032

[DOU]
E.K. van Douwen, Simultaneous extension of continuous functions. Thesis, Free University, Amsterdam, 1975. Cf. MR 52:1612

[D&L]
E. K. van Douwen and D. J. Lutzer, A note on paracompactness in generalized ordered spaces, Proc. AMS, 125(1997), 1237-1245. MR 97f:54039

[D&P]
E.K. van Douwen and Washek F. Pfeffer, Some properties of the Sorgenfrey line and related spaces. Pacific Journ. of Math. 81 (1979), 371 - 377. MR 80h:54027

[ENG]
R. Engelking, General Topology, Sigma Series in Pure Mathematics, 6, Heldermann, Berlin, revised ed., 1989. MR 91c:54001

[F&S]
W. G. Fleissner and A. M. Stanley, D-spaces, Topology and Appl., 114(2001), 261-271. MR 2002e:54013

[GRO]
A. Grothendieck, Critères de compacité dans les espaces fonctionnels généraux, Amer. J. Math. (74) (1952), 168-186. MR 13:857e

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54C35, 54D20, 54C60

Retrieve articles in all Journals with MSC (2000): 54C35, 54D20, 54C60

Additional Information:

Raushan Z. Buzyakova
Affiliation: Department of Mathematics, Brooklyn College, Brooklyn, New York 11210
Email: RaushanB@brooklyn.cuny.edu

DOI: 10.1090/S0002-9939-04-07472-6
PII: S 0002-9939(04)07472-6
Keywords: $C_p(X)$, $D$-space
Received by editor(s): April 21, 2003
Received by editor(s) in revised form: July 31, 2003
Posted: May 20, 2004
Additional Notes: The author's research was supported by PSC-CUNY grant 64457-00 33.
Dedicated: To my teacher Alexander Arhangel'skii for his $65^{\textit{th}}$ birthday
Communicated by: Alan Dow
Copyright of article: Copyright 2004, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google