Monotone principle of forked points and its consequences
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...
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University of Kragujevac, Faculty of Technical Sciences Čačak
2015-01-01
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| Series: | Mathematica Moravica |
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| Online Access: | http://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2015/1450-59321502113T.pdf |
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| author | Tašković Milan R. |
| author_facet | Tašković Milan R. |
| author_sort | Tašković Milan R. |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3e04137f74284bd090dcab2674c3c367 |
| institution | OA Journals |
| issn | 1450-5932 2560-5542 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | University of Kragujevac, Faculty of Technical Sciences Čačak |
| record_format | Article |
| series | Mathematica Moravica |
| spelling | doaj-art-3e04137f74284bd090dcab2674c3c3672025-08-20T01:54:38ZengUniversity of Kragujevac, Faculty of Technical Sciences ČačakMathematica Moravica1450-59322560-55422015-01-011921131241450-59321502113TMonotone principle of forked points and its consequencesTašković Milan R.0Faculty of Mathematics, BelgradeThis 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.http://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2015/1450-59321502113T.pdfthe axiom of infinite choiceZermelo's axiom of choiceLemma of infinite maximalityZorn's lemmaFoundation of the fixed point theoryfixed point theoremstopological spacesForked monotone principlesBrouwer theoremSchauder theoremforks theory |
| spellingShingle | Tašković Milan R. Monotone principle of forked points and its consequences Mathematica Moravica the axiom of infinite choice Zermelo's axiom of choice Lemma of infinite maximality Zorn's lemma Foundation of the fixed point theory fixed point theorems topological spaces Forked monotone principles Brouwer theorem Schauder theorem forks theory |
| title | Monotone principle of forked points and its consequences |
| title_full | Monotone principle of forked points and its consequences |
| title_fullStr | Monotone principle of forked points and its consequences |
| title_full_unstemmed | Monotone principle of forked points and its consequences |
| title_short | Monotone principle of forked points and its consequences |
| title_sort | monotone principle of forked points and its consequences |
| topic | the axiom of infinite choice Zermelo's axiom of choice Lemma of infinite maximality Zorn's lemma Foundation of the fixed point theory fixed point theorems topological spaces Forked monotone principles Brouwer theorem Schauder theorem forks theory |
| url | http://scindeks-clanci.ceon.rs/data/pdf/1450-5932/2015/1450-59321502113T.pdf |
| work_keys_str_mv | AT taskovicmilanr monotoneprincipleofforkedpointsanditsconsequences |