Monotone Principle of Forked Points and Its Consequences
Mathematica Moravica, Tome 19 (2015) no. 2.
Voir la notice de l'article dans eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
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. Zermelo [Neuer Beweis für die Möglichkeit einer Wohlordung, Math. Annalen, 65 (1908), 107-128; translated in van Heijenoort 1967, 183-198], and by M. Ta s kov i c [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.
Mots-clés :
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
@article{MM3_2015_19_2_a8,
author = {Milan Taskovi\'c},
title = {Monotone {Principle} of {Forked} {Points} and {Its} {Consequences}},
journal = {Mathematica Moravica},
pages = {113 - 124},
publisher = {mathdoc},
volume = {19},
number = {2},
year = {2015},
url = {https://geodesic-test.mathdoc.fr/item/MM3_2015_19_2_a8/}
}
Milan Tasković. Monotone Principle of Forked Points and Its Consequences. Mathematica Moravica, Tome 19 (2015) no. 2. https://geodesic-test.mathdoc.fr/item/MM3_2015_19_2_a8/