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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On imbedding finite-dimensional metric spaces


Author: Stephen Leon Lipscomb
Journal: Trans. Amer. Math. Soc. 211 (1975), 143-160
MSC: Primary 54F45
DOI: https://doi.org/10.1090/S0002-9947-1975-0380751-8
MathSciNet review: 0380751
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Abstract | References | Similar Articles | Additional Information

Abstract: The classical imbedding theorem in dimension theory gives a nice topological characterization of separable metric spaces of finite covering dimension. The longstanding problem of obtaining an analogous theorem for the nonseparable case is solved.


References [Enhancements On Off] (What's this?)

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  • [2] S. Lipscomb, A universal one-dimensional metric space, TOPO 72-- General Topology and Its Applications, Second Pittsburgh Internat. Conf., Lecture Notes in Math., vol. 378, Springer-Verlag, New York, 1974. MR 0358738 (50:11197)
  • [3] J. Nagata, A survey of dimension theory, General Topology and Its Relations to Modern Analysis and Algebra II, (Proc. Second Prague Sympos., 1966), Academia, Prague, 1967. MR 0232362 (38:687)
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  • [6] G. Nöbeling, Über eine n-dimensionale Universalmenge im $ {R_{2n + 1'}}$, Math. Ann. 104 (1930), 71-80.
  • [7] P. Ostrand, Covering dimension in general spaces, General Topology and Appl. 1 (1971), no. 3, 209-221. MR 44 #5937. MR 0288741 (44:5937)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0380751-8
Keywords: Covering dimension, imbedding finite-dimensional metric spaces, Baire's zero-dimensional space, perfect images of zero-dimensional spaces, Cantor's space, decompositions of topological spaces
Article copyright: © Copyright 1975 American Mathematical Society

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