The dimension of inverse limits

Charalambous, M. G.

doi:10.1090/S0002-9939-1976-0410696-2

The dimension of inverse limits
HTML articles powered by AMS MathViewer

by M. G. Charalambous PDF

Proc. Amer. Math. Soc. 58 (1976), 289-295 Request permission

Abstract:

A result is obtained concerning the dimension of inverse limits of uniform spaces from which several propositions follow that improve earlier results by various authors.

References

Nicolas Bourbaki, Elements of mathematics. General topology. Part 1, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0205210
M. G. Charalambous, A new covering dimension function for uniform spaces. 2, J. London Math. Soc. (2) 11 (1975), no. part, 137–143. MR 375258, DOI 10.1112/jlms/s2-11.2.137

Uniformity-dependent dimension functions

Howard Cook and Ben Fitzpatrick Jr., Inverse limits of perfectly normal spaces, Proc. Amer. Math. Soc. 19 (1968), 189–192. MR 220240, DOI 10.1090/S0002-9939-1968-0220240-6
R. Engelking, On functions defined on Cartesian products, Fund. Math. 59 (1966), 221–231. MR 203697, DOI 10.4064/fm-59-2-221-231
Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
J. R. Isbell, Uniform spaces, Mathematical Surveys, No. 12, American Mathematical Society, Providence, R.I., 1964. MR 0170323
V. Kljušin, Perfect mappings of paracompact spaces, Dokl. Akad. Nauk SSSR 159 (1964), 734–737 (Russian). MR 0173234
Sibe Mardešić, On covering dimension and inverse limits of compact spaces, Illinois J. Math. 4 (1960), 278–291. MR 116306
E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375–376. MR 152985, DOI 10.1090/S0002-9904-1963-10931-3
Kiiti Morita, On the dimension of the product of Tychonoff spaces, General Topology and Appl. 3 (1973), 125–133. MR 321041
Keiô Nagami, Dimension theory, Pure and Applied Mathematics, Vol. 37, Academic Press, New York-London, 1970. With an appendix by Yukihiro Kodama. MR 0271918
Keiô Nagami, Countable paracompactness of inverse limits and products, Fund. Math. 73 (1971/72), no. 3, 261–270. MR 301688, DOI 10.4064/fm-73-3-261-270
Peter Nyikos, Prabir Roy’s space $\Delta$ is not $N$-compact, General Topology and Appl. 3 (1973), 197–210. MR 324657
B. Pasynkov, On $\omega$-mappings and inverse spectra, Dokl. Akad. Nauk SSSR 150 (1963), 488–491 (Russian). MR 0152984
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). MR 0214035
A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948), 977–982. MR 26802, DOI 10.1090/S0002-9904-1948-09118-2
Jun Terasawa, On the zero-dimensionality of some non-normal product spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 11 (1972), 167–174. MR 310850
N. Noble and Milton Ulmer, Factoring functions on Cartesian products, Trans. Amer. Math. Soc. 163 (1972), 329–339. MR 288721, DOI 10.1090/S0002-9947-1972-0288721-2
Zdeněk Frolík, A note on metric-fine spaces, Proc. Amer. Math. Soc. 46 (1974), 111–119. MR 358704, DOI 10.1090/S0002-9939-1974-0358704-X
Anthony W. Hager, Some nearly fine uniform spaces, Proc. London Math. Soc. (3) 28 (1974), 517–546. MR 397670, DOI 10.1112/plms/s3-28.3.517