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
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
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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
Additional Information
- © Copyright 1975 American Mathematical Society
- 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