An alternative proof of the Tychonoff theorem

• Autorzy: Ercan Z.
• Języki publikacji: EN

Abstrakty

EN

An alternative proof of the Tychonoff Theorem, is presented via the Riesz homomorphism.

Słowa kluczowe

EN

Riesz homomorphism; Tychonoff theorem

PL

homomorfizm Riesza; teoria Tychonoffa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 4
• Strony: 901--903
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Ercan Z.

• Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey

Bibliografia

• [1] E. Čech, On bicompact spaces, Ann. Math. 38 (1937), 823-844.
• [2] P. R. Chernoff, A simple proof of the Tychonoff's theorem via nets, Amer. Math. Monthly, 99, no. 10 (1992), 932-934.
• [3] E. De Jonge and A. C. M. Van Rooij, Introduction to Riesz Spaces, Mathematisch Centrum, 1977.
• [4] R. Engelking, General Topology, Berlin-Heldermann, 1989.
• [5] J. L. Kelley, The Tychonoff product theorem implies the axiom of choice, Fund. Math. 37 (1950), 75-76.
• [6] J. L. Kelley, General Topology, 2nd Printing, Springer-Verlag, New York, 1975.
• [7] A. W. J. Luxemburg and A. C. Zaanen, Riesz Spaces I, North-Holland, Amsterdam, 1971.
• [8] J. E. Rubin and D. S. Scott, Some topological theorems equivalent to the axiom of choice, Bull. Amer. Math. Soc., 60 (1935), 389.
• [9] A. Tychonoff, Uber die topologische Erweterung von Raumen, Math. Annalen, 102 (1929), 544-56 1.
• [10] D. G. Wright, Tychonoff's theorem, Proc. Amer. Math. Soc. 120, no. 3 (1994), 985-987.