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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the dimensional properties of Stone-Čech remainder of $P_ 0$-spaces
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by H. Attia PDF
Proc. Amer. Math. Soc. 121 (1994), 1245-1249 Request permission

Abstract:

A space X is called a ${P_0}$-space if there exists a perfect mapping f from X onto a metric space Y such that $\dim f = \sup \{ {f^{ - 1}}(y):y \in Y\} = 0$. We prove that the ${P_0}$-space X is almost weakly infinite dimensional iff the remainder $\beta X\backslash X$ of the Stone-Čech compactification $\beta X$ of X is A-weakly infinite dimensional. Furthermore we prove that $\Delta (\beta X\backslash X = {\text {ind}}(\beta X\backslash X) = {\text {Ind}}(\beta X\backslash X) = \dim (\beta X\backslash X)$ for the ${P_0}$-space X.
References
    P. S. Alexcandroff and B. A. Pasynkov, Introduction to dimension theory, Nauka, Moscow, 1973. (Russian)
  • A. Arhangel′skiĭ, The factorization of mappings by weight and dimension, Dokl. Akad. Nauk SSSR 174 (1967), 1243–1246 (Russian). MR 0216472
  • A. V. Arhangel′skiĭ, A class of spaces which contains all metric and all locally compact spaces, Mat. Sb. (N.S.) 67 (109) (1965), 55–88 (Russian). MR 0190889
  • A. V. Arhangel′skiĭ, Open and close-to-open mappings. Relations among spaces, Trudy Moskov. Mat. Obšč. 15 (1966), 181–223 (Russian). MR 0206909
  • M. M. Čoban, Topological structure of subsets of topological groups and their factor spaces, Cb. Mat. Recearsh Keshenev, Science, 44 (1977), 117-163. (Russian)
  • M. M. Čoban and H. Attia, On the dimension of remainders of extensions of normal spaces, Topology Appl. 36 (1990), no. 2, 97–109. Seminar on General Topology and Topological Algebra (Moscow, 1988/1989). MR 1068163, DOI 10.1016/0166-8641(90)90002-J
  • R. Engleking, Dimension theory, Warszawa, Oxford and New York, 1978.
  • Melvin Henriksen and J. R. Isbell, Some properties of compactifications, Duke Math. J. 25 (1958), 83–105. MR 96196
  • Stoyan Ĭ. Nedev, Selection and factorization theorems for set-valued mappings, Serdica 6 (1980), no. 4, 291–317 (1981). MR 644284
  • B. A. Pasynkov, Factorization theorems in dimension theory, Uspekhi Mat. Nauk 36 (1981), no. 3(219), 147–175, 256 (Russian). MR 622723
  • B. A. Pasynkov, The dimension of spaces with a bicompact transformation group, Uspehi Mat. Nauk 31 (1976), no. 5(191), 112–120 (Russian). MR 0445470
  • V. I. Ponomarev, Paracompacta: their projection spectra and continuous mappings, Mat. Sb. (N.S.) 60 (102) (1963), 89–119 (Russian). MR 0152980
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 121 (1994), 1245-1249
  • MSC: Primary 54F45; Secondary 54D40, 54E18
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1156462-5
  • MathSciNet review: 1156462