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The dimension of inverse limits. (English) Zbl 0348.54029


MSC:

54F45 Dimension theory in general topology
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54E15 Uniform structures and generalizations
54G20 Counterexamples in general topology
54B35 Spectra in general topology
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References:

[1] Nicolas Bourbaki, Elements of mathematics. General topology. Part 1, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. Nicolas Bourbaki, Elements of mathematics. General topology. Part 2, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966.
[2] M. G. Charalambous, A new covering dimension function for uniform spaces. part 2, J. London Math. Soc. (2) 11 (1975), no. part 2, 137 – 143. · Zbl 0306.54048
[3] -, Uniformity-dependent dimension functions (to appear). · Zbl 0214.21302
[4] Howard Cook and Ben Fitzpatrick Jr., Inverse limits of perfectly normal spaces, Proc. Amer. Math. Soc. 19 (1968), 189 – 192. · Zbl 0157.29201
[5] R. Engelking, On functions defined on Cartesian products, Fund. Math. 59 (1966), 221 – 231. · Zbl 0158.41203
[6] Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, v. 4, Princeton University Press, Princeton, N. J., 1941. · Zbl 0060.39808
[7] J. R. Isbell, Uniform spaces, Mathematical Surveys, No. 12, American Mathematical Society, Providence, R.I., 1964. · Zbl 0124.15601
[8] V. Kljušin, Perfect mappings of paracompact spaces, Dokl. Akad. Nauk SSSR 159 (1964), 734 – 737 (Russian).
[9] Sibe Mardešić, On covering dimension and inverse limits of compact spaces, Illinois J. Math. 4 (1960), 278 – 291. · Zbl 0094.16902
[10] 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
[11] Kiiti Morita, On the dimension of the product of Tychonoff spaces, General Topology and Appl. 3 (1973), 125 – 133. · Zbl 0258.54034
[12] 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
[13] Keiô Nagami, Countable paracompactness of inverse limits and products, Fund. Math. 73 (1971/72), no. 3, 261 – 270. · Zbl 0226.54005
[14] Peter Nyikos, Prabir Roy’s space \Delta is not \?-compact, General Topology and Appl. 3 (1973), 197 – 210. · Zbl 0265.54042
[15] B. Pasynkov, On \?-mappings and inverse spectra, Dokl. Akad. Nauk SSSR 150 (1963), 488 – 491 (Russian). · Zbl 0144.44503
[16] Ju. M. Smirnov, On the dimension of remainders in bicompact extensions of proximity and topological spaces. II, Mat. Sb. (N.S.) 71 (113) (1966), 454 – 482 (Russian).
[17] A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948), 977 – 982. · Zbl 0032.31403
[18] Jun Terasawa, On the zero-dimensionality of some non-normal product spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 11 (1972), 167 – 174. · Zbl 0253.54032
[19] N. Noble and Milton Ulmer, Factoring functions on Cartesian products, Trans. Amer. Math. Soc. 163 (1972), 329 – 339. · Zbl 0207.21302
[20] Zdeněk Frolík, A note on metric-fine spaces, Proc. Amer. Math. Soc. 46 (1974), 111 – 119. · Zbl 0301.54033
[21] Anthony W. Hager, Some nearly fine uniform spaces, Proc. London Math. Soc. (3) 28 (1974), 517 – 546. · Zbl 0284.54017
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