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On imbedding finite-dimensional metric spaces
Author:
Stephen Leon Lipscomb
Journal:
Trans. Amer. Math. Soc. 211 (1975), 143-160
MSC:
Primary 54F45
MathSciNet review:
0380751
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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.
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S. Lipscomb, Imbedding one-dimensional metric spaces, Dissertation, University of Virginia, Charlottesville, Va., 1973.
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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
(50 #11197)
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Jun-iti
Nagata, A survey of dimension theory, (Proc. Second Prague
Topological Sympos., 1966) Academia, Prague, 1967,
pp. 259–270. MR 0232362
(38 #687)
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Jun-iti
Nagata, A remark on general imbedding theorems in dimension
theory, Proc. Japan Acad. 39 (1963), 197–199.
MR
0164319 (29 #1616)
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-, Modern dimension theory, Bibliotheca Math., vol. 6, Interscience, New York, 1965. MR 34 #8380.
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G. Nöbeling, Über eine n-dimensionale Universalmenge im
 , Math. Ann. 104 (1930), 71-80.
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Phillip
A. Ostrand, Covering dimension in general spaces, General
Topology and Appl. 1 (1971), no. 3, 209–221. MR 0288741
(44 #5937)
- [1]
- S. Lipscomb, Imbedding one-dimensional metric spaces, Dissertation, University of Virginia, Charlottesville, Va., 1973.
- [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)
- [4]
- -, A remark on general imbedding theorems in dimension theory, Proc. Japan Acad. 39 (1963), 197-199. MR 29 #1616. MR 0164319 (29:1616)
- [5]
- -, Modern dimension theory, Bibliotheca Math., vol. 6, Interscience, New York, 1965. MR 34 #8380.
- [6]
- G. Nöbeling, Über eine n-dimensionale Universalmenge im , 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:
http://dx.doi.org/10.1090/S0002-9947-1975-0380751-8
PII:
S 0002-9947(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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