CHAILOS, GEORGE
(2017)
*GROUP INVARIANT BOUNDED LINEAR FUNCTIONS ON DEDEKIND COMPLETE TOTALLY ORDERED RIESZ SPACES.*
Asian Journal of Mathematics and Computer Research, 17 (4).
pp. 204-211.

## 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.

Item Type: | Article |
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Subjects: | Opene Prints > Mathematical Science |

Depositing User: | Managing Editor |

Date Deposited: | 28 Dec 2023 04:43 |

Last Modified: | 28 Dec 2023 04:43 |

URI: | http://geographical.go2journals.com/id/eprint/3287 |