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Some continuous decompositions of the space En

  • Van Ny Kyong
Article

Abstract

The main result proved is the following. Let E f (n) (n > 1) be a continuous decomposition of E(n) into points and zero-dimensional compact setsξλ. If\(P* = \bigcup\limits_\lambda {\xi _\lambda } \) is compact and dimf(P*) = 0, then the spacef(En) can be imbedded in E(n+1).

Keywords

Continuous Decomposition 
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Literature cited

  1. 1.
    L. V. Keldysh, “The imbedding in En and in En+1 of certain monotonic images of En,“ Matem. Sb.,57 (99), 95–104 (1962).Google Scholar
  2. 2.
    V. Klee, “Some topological properties of convex sets,“ Trans. Amer. Math. Soc.,78, 30–45 (1955).Google Scholar
  3. 3.
    W. R. Alford and R. B. Sher, “Defining sequences for compact O-dimensional decomposition of En,“ Bull. Acad. Polon. Sci., Série Math., Ast., Phys.,17, No. 4, 209–212 (1969).Google Scholar

Copyright information

© Consultants Bureau 1972

Authors and Affiliations

  • Van Ny Kyong
    • 1
  1. 1.V. A. Steklov Mathematics InstituteAcademy of Sciences of the USSRUSSR

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