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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


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.
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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:
  • MathSciNet review: 1156462