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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On imbedding finite-dimensional metric spaces
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by Stephen Leon Lipscomb PDF
Trans. Amer. Math. Soc. 211 (1975), 143-160 Request permission


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.
    S. Lipscomb, Imbedding one-dimensional metric spaces, Dissertation, University of Virginia, Charlottesville, Va., 1973.
  • 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), Lecture Notes in Math., Vol. 378, Springer, Berlin, 1974, pp. 248–257. MR 0358738
  • 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
  • Jun-iti Nagata, A remark on general imbedding theorems in dimension theory, Proc. Japan Acad. 39 (1963), 197–199. MR 164319
  • —, Modern dimension theory, Bibliotheca Math., vol. 6, Interscience, New York, 1965. MR 34 #8380. G. Nöbeling, Über eine n-dimensionale Universalmenge im ${R_{2n + 1’}}$, Math. Ann. 104 (1930), 71-80.
  • Phillip A. Ostrand, Covering dimension in general spaces, General Topology and Appl. 1 (1971), no. 3, 209–221. MR 288741, DOI 10.1016/0016-660X(71)90093-6
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 211 (1975), 143-160
  • MSC: Primary 54F45
  • DOI:
  • MathSciNet review: 0380751