Remarks on maps of inverse limits
Abstract
The aim of this note is to give a short proof of the Ščepin theorem concerning maps of inverse limits. This theorem was generalized by several authors; see e.g. W. Kulpa [5], A. Archangelskii [1] and M.G. Tkačenko [7], [8].
Our method of the proof gives also the most general version of the Ščepin theorem due to Tkačenko. It can be also applied for obtaining in a very general setting the theorem of H.H. Corson and J.R. Isbell [3], [4] concerning maps from products.
References
2. R. Engelking, General topology, PWN, Warszawa, 1977.
3. H.H. Corson, Normality in subsets of product spaces, Amer. J. Math. 81 (1959), 785-796.
4. H.H. Corson, J.R. Isbell, Some properties of strong uniformities, Quart. J. Math. Oxford 11 (1960), 17-33.
5. W. Kulpa, Factorization theorems and properties of the covering type, Prace Naukowe Uniwersytetu Śląskiego w Katowicach 350, Uniwersytet Śląski, Katowice, 1980.
6. E.Б. Щeпин, Toпoлoгия пpeдeльных пpocтpaнcтв нecчeтных cпeктpoв, Uspekhi Mat. Nauk. 31 (1976), 191-226.
7. M.G. Tkačenko, Some results on inverse spectra 1, Comment. Math. Univ. Carolin. 22 (1981), 621-633.
8. M.G. Tkačenko, Some results on inverse spectra 2, Comment. Math. Univ. Carolin. 22 (1981), 819-841.
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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