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2015, vol. 19, br. 2, str. 113-124
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Monotone principle of forked points and its consequences
(naslov ne postoji na srpskom)
Sažetak
(ne postoji na srpskom)
This paper presents applications of the Axiom of Infinite Choice: Given any set P, there exist at least countable choice functions or there exist at least finite choice functions. The author continues herein with the further study of two papers of the Axiom of Choice in order by E. Ze rme l o [Neuer Beweis für die Möglichkeit einer Wohlordung, Math. Annalen, 65 (1908), 107-128; translated in van Heijenoort 1967, 183-198], and by M. Taskovic [The axiom of choice, fixed point theorems, and inductive ordered sets, Proc. Amer. Math. Soc., 116 (1992), 897-904]. Monotone principle of forked points is a direct consequence of the Axiom of Infinite Choice, i.e., of the Lemma of Infinite Maximality! Brouwer and Schauder theorems are two direct censequences of the monotone principle od forked points.
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Reference
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Taskovic, M.R. (2005) Theory of transversal point, spaces and forks. u: Fundamental Elements and Applications: Monographs of a new mathematical theory, Beograd: VIZ, In Serbian, 1054 pages. English summary: 1001-1022
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Tasković, M.R. (2010) Transversal theory of fixed point, fixed apices, and forked points. Mathematica Moravica, vol. 14, br. 2, str. 19-97
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Zermelo, E. (1907) Neuer Beweis für die Möglichkeit einer Wohlordnun. Mathematische Annalen, 65(1): 107-128
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Zermelo, E. (1904) Beweis dass jede Menge wohlgeordnet werden kann, (Aus einem an Herrn Hilbert gerichteten Briefe). Mathematische Annalen, 59(4): 514-516
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Zorn, M. (1944) Idempotency of infinite cardinals. Univ. Calif. Publ. in Math., Seminar Reports (Los Angeles), 2, 9-12
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Zorn, M. (1935) A remark on method in transfinite algebra. Bulletin of the American Mathematical Society, 41(10): 667-671
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