Hereditary D-property of function spaces over compacta
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- by Raushan Z. Buzyakova PDF
- Proc. Amer. Math. Soc. 132 (2004), 3433-3439 Request permission
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 Matveevās question. A connection between the $D$-property and Baturovās and Grothendieckās classical theorems about function spaces over compacta is established.References
- A. V. Arkhangelā²skiÄ, Topological function spaces, Mathematics and its Applications (Soviet Series), vol. 78, Kluwer Academic Publishers Group, Dordrecht, 1992. Translated from the Russian by R. A. M. Hoksbergen. MR 1144519, DOI 10.1007/978-94-011-2598-7
- A. Arhangelskii and R. Buzyakova, Addition theorems and $D$-spaces, Comment. Math. Universitatis Carolinae 43, 4(2002), 653-663.
- D. P. Baturov, Subspaces of function spaces, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 4 (1987), 66ā69 (Russian). MR 913076
- Raushan Z. Buzyakova, On $D$-property of strong $\Sigma$ spaces, Comment. Math. Univ. Carolin. 43 (2002), no.Ā 3, 493ā495. MR 1920524
- Carlos R. Borges and Albert C. Wehrly, A study of $D$-spaces, Topology Proc. 16 (1991), 7ā15. MR 1206448
- Carlos R. Borges and Albert C. Wehrly, Another study of $D$-spaces, Questions Answers Gen. Topology 14 (1996), no.Ā 1, 73ā76. MR 1384056
- Carlos R. Borges and Albert C. Wehrly, Correction: āAnother study of $D$-spacesā [Questions Answers Gen. Topology 14 (1996), no. 1, 73ā76; MR1384056 (96m:54033)], Questions Answers Gen. Topology 16 (1998), no.Ā 1, 77ā78. MR 1614761
- Peter de Caux, Yet another property of the Sorgenfrey plane, Topology Proc. 6 (1981), no.Ā 1, 31ā43 (1982). MR 650479
- Eric K. van Douwen, Simultaneous linear extension of continuous functions, General Topology and Appl. 5 (1975), no.Ā 4, 297ā319. MR 380715
- Eric K. van Douwen and David J. Lutzer, A note on paracompactness in generalized ordered spaces, Proc. Amer. Math. Soc. 125 (1997), no.Ā 4, 1237ā1245. MR 1396999, DOI 10.1090/S0002-9939-97-03902-6
- Eric K. van Douwen and Washek F. Pfeffer, Some properties of the Sorgenfrey line and related spaces, Pacific J. Math. 81 (1979), no.Ā 2, 371ā377. MR 547605
- Ryszard Engelking, General topology, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR 1039321
- William G. Fleissner and Adrienne M. Stanley, $D$-spaces, Topology Appl. 114 (2001), no.Ā 3, 261ā271. MR 1838325, DOI 10.1016/S0166-8641(00)00042-0
- C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623ā627. MR 13
Additional Information
- Raushan Z. Buzyakova
- Affiliation: Department of Mathematics, Brooklyn College, Brooklyn, New York 11210
- Email: RaushanB@brooklyn.cuny.edu
- 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 authorās research was supported by PSC-CUNY grant 64457-00 33.
- Communicated by: Alan Dow
- © Copyright 2004 American Mathematical Society
- 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
- MathSciNet review: 2073321
Dedicated: To my teacher Alexander Arhangelāskii for his $65^{\textit {th}}$ birthday