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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?)

  • [1] S. Lipscomb, Imbedding one-dimensional metric spaces, Dissertation, University of Virginia, Charlottesville, Va., 1973.
  • [2] Stephen Leon Lipscomb, A universal one-dimensional metric space, TOPO 72—general topology and its applications (Proc. Second Pittsburgh Internat. Conf., Pittsburgh, Pa., 1972; dedicated to the memory of Johannes H. de Groot), Springer, Berlin, 1974, pp. 248–257. Lecture Notes in Math., Vol. 378. MR 0358738
  • [3] Jun-iti Nagata, A survey of dimension theory, General Topology and its Relations to Modern Analysis and Algebra, II (Proc. Second Prague Topological Sympos., 1966) Academia, Prague, 1967, pp. 259–270. MR 0232362
  • [4] Jun-iti Nagata, A remark on general imbedding theorems in dimension theory, Proc. Japan Acad. 39 (1963), 197–199. MR 0164319
  • [5] -, Modern dimension theory, Bibliotheca Math., vol. 6, Interscience, New York, 1965. MR 34 #8380.
  • [6] G. Nöbeling, Über eine n-dimensionale Universalmenge im $ {R_{2n + 1'}}$, Math. Ann. 104 (1930), 71-80.
  • [7] Phillip A. Ostrand, Covering dimension in general spaces, General Topology and Appl. 1 (1971), no. 3, 209–221. MR 0288741

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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