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On the dimensional properties of Stone-Čech remainder of $ P\sb 0$-spaces


Author: H. Attia
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
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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.


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  • [1] P. S. Alexcandroff and B. A. Pasynkov, Introduction to dimension theory, Nauka, Moscow, 1973. (Russian)
  • [2] A. V. Arhangelskii, Factorization of mappings according to weight and dimension, Dokl. Akad. Nauk SSSR 174 (1967), 1243-1246; English transl. in Soviet Math. Dokl. 8 (1967), 731-734. MR 0216472 (35:7305)
  • [3] -, On a class of spaces containing all metric spaces and all locally compact spaces, Mat. Sb. 67 (109) (1965), 55-88; English transl. in Amer. Math. Soc. Transl. (2) 92 (1970), 1-39. MR 0190889 (32:8299)
  • [4] -, Open and near open mappings. Connections between spaces, Trudy Moscov. Mat. Obshch. 15 (1966), 181-223; English transl. in Trans. Moscow Math. Soc. 15 (1966), 204-250. MR 0206909 (34:6725)
  • [5] M. M. Čoban, Topological structure of subsets of topological groups and their factor spaces, Cb. Mat. Recearsh Keshenev, Science, 44 (1977), 117-163. (Russian)
  • [6] M. M. Čoban and H. Attia, On the dimension of remainders of extensions of normal spaces, Topology Appl. 36 (1990), 97-109. MR 1068163 (91m:54029)
  • [7] R. Engleking, Dimension theory, Warszawa, Oxford and New York, 1978.
  • [8] M. Henriksen and J. Isbell, Some properties of compactifications, Duke Math. J. 25 (1958), 83-103. MR 0096196 (20:2689)
  • [9] S. Nedev, Selection and factorization theorem for set-valued mappings, Serdica 6 (1980), 291-317. MR 644284 (83c:54023)
  • [10] B. A. Pasynkov, Factorization theorems in dimension theory, Uspekhi Mat. Nauk 36 (1981), 147-175. (Russian) MR 622723 (82g:54061)
  • [11] -, On the dimension of the spaces with transformed bicompact groups, Uspekhi Mat. Nauk 31 (1976), 112-120. (Russian) MR 0445470 (56:3810)
  • [12] V. I. Ponamarev, Projective spectra and continuous mappings and paracompacta, Mat. Sb. 60 (1963), 89-119; English transl. in Amer. Math. Soc. Transl. (2) 39 (1964), 133-164. MR 0152980 (27:2951)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1156462-5
Keywords: $ {P_0}$-spaces, dimension, almost weakly infinite dimensional, remainder
Article copyright: © Copyright 1994 American Mathematical Society

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