Infinite dimensional compacta containing no $n$dimensional $\left( {n \geqslant 1} \right)$ subsets
Author:
John J. Walsh
Journal:
Bull. Amer. Math. Soc. 84 (1978), 137138
MSC (1970):
Primary 54F45, 55C10
DOI:
https://doi.org/10.1090/S000299041978144413
MathSciNet review:
0458435
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References  Similar Articles  Additional Information
 P. S. Aleksandrov, Some results in the theory of topological spaces obtained within the last twentyfive years, Russian Math. Surveys 15 (1960), no. 2, 23–83. MR 0119181, https://doi.org/10.1070/RM1960v015n02ABEH004216
 P. S. Aleksandrov, Some fundamental directions in general topology, Uspehi Mat. Nauk 19 (1964), no. 6 (120), 3–46 (Russian). MR 0172230
 R. H. Bing, A hereditarily infinite dimensional space, General Topology and its Relations to Modern Analysis and Algebra, II (Proc. Second Prague Topological Sympos., 1966) Academia, Prague, 1967, pp. 56–62. MR 0233336

[He1] D. W. Henderson, An infinitedimensional compactum with no positivedimensional compact subsets—a simpler construction, Amer. J. Math. 89 (1967), 105121.
 David W. Henderson, Each strongly infinitedimensional compactum contains a hereditarily infinitedimensional compact subset, Amer. J. Math. 89 (1967), 122–123. MR 210073, https://doi.org/10.2307/2373101
 Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, v. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493

[Ko] G. Kozlowski, Images of ANR's, Trans. Amer. Math. Soc. (to appear).

[RSW] L. Rubin, R. Schori and J. Walsh, New Dimensiontheory techniques for constructing infinitedimensional examples (submitted).

[Za] A. V. Zarelua, Construction of strongly infinite dimensional compacta using rings of continuous functions, Soviet Math. Dokl. 15 (1974), 106110.
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Additional Information
DOI:
https://doi.org/10.1090/S000299041978144413