GROUP INVARIANT BOUNDED LINEAR FUNCTIONS ON DEDEKIND COMPLETE TOTALLY ORDERED RIESZ SPACES

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Published: 2017-04-20

Page: 204-211


GEORGE CHAILOS *

Department of Mathematics, University of Nicosia, 1700, Nicosia, Cyprus.

*Author to whom correspondence should be addressed.


Abstract

In this paper we consider the set B of all bounded subsets of V, where V is a totally ordered Dedekind complete Riesz  space equipped with the order topology. We show the existence of nontrivial bounded linear functions on B that are invariant under group actions of the symmetric group of B. To do this, we construct a set of “approximately” group invariant bounded linear functions and we show, using Tychonff’s Theorem (that is equivalent to the Axiom of Choice), that this set has a cluster point. This cluster point is the group invariant bounded linear function on B that we are looking for.

Keywords: Riesz spaces, bounded linear functions, group actions, Tychonoff’s theorem


How to Cite

CHAILOS, G. (2017). GROUP INVARIANT BOUNDED LINEAR FUNCTIONS ON DEDEKIND COMPLETE TOTALLY ORDERED RIESZ SPACES. Asian Journal of Mathematics and Computer Research, 17(4), 204–211. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/966

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