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Abstrakty
The theorem in the title is proven. Applications to product theorems are given.
Wydawca
Rocznik
Tom
Strony
147--152
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
- Department of Mathematics, University of Mississippi, University, MS 38677, U.S.A., mmlabuda@olemiss.edu
Bibliografia
- [1] J. W. Alexander, Ordered sets, complexes and the problem of compactification. Proc. Nat. Acad. Sci. USA 25 (1939), 296-298.
- [2] P. Alexandroff et P. Urysohn, Memoire sur les espaces topologiques compacts, Verh. Kon. Akad. Wetensch. Amsterdam 14 (1929), 1-96.
- [3] P. Alexandroff und H. Hopf, Topologie, Chelsea, New York, 1965 (reprint of the original 1935 edition).
- [4] R. Beattie and H. P. Butzmann, Convergence Structures and Applications to Functional Analysis, Kluwer, 2002.
- [5] N. Bourbaki. Topologie generale, Ch. I, II, 3-me ed., Hermann, Paris, 1961.
- [6] G. Buskes and A. van Rooij, Topological Spaces, Springer, 1997.
- [7] D. E. Cameron, The birth of the Stone-Cech compactification, in: Rings of Continuous Functions, Lecture Notes in Pure and Appl. Math. 95, Dekker, New York, 1985, 67-78.
- [8] E. Cech, On bicompact spaces, Ann. of Math. 38 (1937), 823-844.
- [9] C. Chevalley and 0. Prink, Bicompactness of Cartesian products, Bull. Amer. Math. Soc. 47 (1941), 612-614.
- [10] B. L. Davis and I. Labuda, Infinite products of filters, Math. Slovaca, to appear.
- [11] —, —, Unity of compactness, preprint, 2005, submitted.
- [12] S. Dolecki et G. H. Greco, Families pseudotopologiques de filtres et compacite, C. R. Acad. Sci. Paris 296 (1983), 211-214.
- [13] L. Drewnowski and I. Labuda, On minimal upper semicontinuous compact-valued maps, Rocky Mountain J. Math. 20 (1990), 737-752.
- [14] R. Engelking, General Topology, PWN-Polish Sci. Publ., Warszawa, 1977.
- [15] M. Katetov and P. Simon (eds.), The Mathematical Legacy of Eduard Cech, Birkhäuser, 1993.
- [16] J. L. Kelley, The Tychonoff product theorem implies the axiom of choice. Fund. Math. 37 (1950), 75-76.
- [17] —, General Topology, Van Nostrand, 1955.
- [18] I. Labuda, Compactoidness, Rocky Mountain J. Math. 36 (2006), 555-574.
- [19] B. J. Pettis, Cluster sets of nets, Proc. Amer. Math. Soc. 22 (1969), 386-391.
- [20] W. Rudin, Functional Analysis, McGraw-Hill, 1973.
- [21] A. Tychonoff, Über topologische Erweiterung von Raümen, Math. Ann. 102 (1930), 544-561.
- [22] A. Tychonoff, Em, Fixpunktsatz, ibid. 111 (1935), 767-776.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0011-0024