Hereditary D-property of function spaces over compacta
Author:
Raushan Z. Buzyakova
Journal:
Proc. Amer. Math. Soc. 132 (2004), 3433-3439
MSC (2000):
Primary 54C35, 54D20, 54C60
DOI:
https://doi.org/10.1090/S0002-9939-04-07472-6
Published electronically:
May 20, 2004
MathSciNet review:
2073321
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Abstract | References | Similar Articles | Additional Information
Abstract: It is shown that if is compact then every subspace of
is a
-space in the sense of E. van Douwen, which positively answers Matveev's question. A connection between the
-property and Baturov's and Grothendieck's classical theorems about function spaces over compacta is established.
- [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
-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
-property of strong
-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
-spaces. Topology Proc. 16 (1991), 7 - 15. MR 94a:54059
- [B&W2]
C.R. Borges and A.C. Wehrly, Another study of
-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
-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
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Additional Information
Raushan Z. Buzyakova
Affiliation:
Department of Mathematics, Brooklyn College, Brooklyn, New York 11210
Email:
RaushanB@brooklyn.cuny.edu
DOI:
https://doi.org/10.1090/S0002-9939-04-07472-6
Keywords:
$C_p(X)$,
$D$-space
Received by editor(s):
April 21, 2003
Received by editor(s) in revised form:
July 31, 2003
Published electronically:
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 $65^{th}$ birthday
Communicated by:
Alan Dow
Article copyright:
© Copyright 2004
American Mathematical Society