Pol, Roman A weakly infinite-dimensional compactum which is not countable- dimensional. (English) Zbl 0469.54014 Proc. Am. Math. Soc. 82, 634-636 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 31 Documents MSC: 54E45 Compact (locally compact) metric spaces 54F45 Dimension theory in general topology Keywords:weakly infinite-dimensional compactum; essential map; Hilbert cube; not countable-dimensional PDF BibTeX XML Cite \textit{R. Pol}, Proc. Am. Math. Soc. 82, 634--636 (1981; Zbl 0469.54014) Full Text: DOI OpenURL References: [1] P. S. Aleksandrov, The present status of the theory of dimension, Uspehi Matem. Nauk (N.S.) 6 (1951), no. 4(45), 43 – 68 (Russian). [2] P. S. Aleksandrov, Some results in the theory of topological spaces obtained within the last twenty-five years, Russian Math. Surveys 15 (1960), no. 2, 23 – 83. · Zbl 0142.20802 [3] Введение в теорию размерности: Введение в теорию топологических пространств и общую теорию размерности., Издат. ”Наука”, Мосцощ, 1973 (Руссиан). [4] N. Bourbaki, Éléments de mathématique. I: Les structures fondamentales de l’analyse. Fascicule VIII. Livre III: Topologie générale. Chapitre 9: Utilisation des nombres réels en topologie générale, Deuxième édition revue et augmentée. Actualités Scientifiques et Industrielles, No. 1045, Hermann, Paris, 1958 (French). · Zbl 0085.37103 [5] R. Engelking, Transfinite dimension, Surveys in general topology, Academic Press, New York-London-Toronto, Ont., 1980, pp. 131 – 161. · Zbl 0447.54046 [6] V. V. Fedorčuk, Infinite-dimensional compact Hausdorff spaces, Izv. Akad. Nauk SSSR Ser. Mat. 42 (1978); English transl. in Math. USSR Izv. 13 (1979), 445-460. · Zbl 0423.54024 [7] David W. Henderson, A lower bound for transfinite dimension, Fund. Math. 63 (1968), 167 – 173. · Zbl 0167.51301 [8] W. Hurewicz and H. Wallman, Dimension theory, Van Nostrand, Princeton, N. J., 1948. · Zbl 0036.12501 [9] Bronisław Knaster, Sur les coupures biconnexes des espaces euclidiens de dimension \?>1 arbitraire, Rec. Math. [Mat. Sbornik] N.S. 19(61) (1946), 9 – 18 (Russian, with French summary). · Zbl 0061.40104 [10] K. Kuratowski, Sur le prolongement des fonctions continues et les transformations en polytopes, Fund. Math. 24 (1935), 258-268. · JFM 61.1367.02 [11] -, Topology. Vol. II, PWN, Warsaw, 1968. [12] A. Lelek, Dimension inequalities for unions and mappings of separable metric spaces, Colloq. Math. 23 (1971), 69 – 91. · Zbl 0219.54032 [13] S. Mazurkiewicz, Sur les problèmes \( \kappa \) et \( \lambda \) de Urysohn, Fund. Math. 10 (1927), 311-319. · JFM 53.0563.02 [14] E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375 – 376. · Zbl 0114.38904 [15] Keiô Nagami, Dimension theory, With an appendix by Yukihiro Kodama. Pure and Applied Mathematics, Vol. 37, Academic Press, New York-London, 1970. · Zbl 0224.54060 [16] Roman Pol, On classification of weakly infinite-dimensional compacta, Fund. Math. 116 (1983), no. 3, 169 – 188. · Zbl 0571.54030 [17] -, A remark on \( A\)-weakly infinite-dimensional spaces, General Topology Appl. (to appear). [18] Leonard R. Rubin, R. M. Schori, and John J. Walsh, New dimension-theory techniques for constructing infinite-dimensional examples, General Topology Appl. 10 (1979), no. 1, 93 – 102. · Zbl 0413.54042 [19] Yu. Smirnov, On dimensional properties of infinite-dimensional spaces, General Topology and its Relations to Modern Analysis and Algebra (Proc. Sympos., Prague, 1961) Academic Press, New York; Publ. House Czech. Acad. Sci., Prague, 1962, pp. 334 – 336. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.