APPLICATIONS OF GENERALIZED ZORN’S LEMMA

Sehie Park

APPLICATIONS OF GENERALIZED ZORN’S LEMMA

Authors

Sehie Park The National Academy of Sciences, Republic of Korea, Seoul 06579; Department of Mathematical Sciences, Seoul National University, Seoul 08826

Keywords:

fixed point theorem, preorder, metric space, fixed point, stationary point, maximal element

Abstract

In the present article, by applying our 2013 Metatheorem and the Brøndsted-Jachymski Principle, we obtain various forms generalizations of Zorn’s Lemma and their applications. Such examples are our version of the Zermelo fixed point theorem, equivalent formulations of the Caristi fixed point theorem, and Jachymski’s 2003 theorem on equivalent conditions when fixed point sets are same to periodic point sets.