### 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 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.

.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.

Original language | English |
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Pages (from-to) | 206-211 |

Number of pages | 6 |

Journal | Asian Journal of Mathematics and Computer Research |

Volume | 7 |

Issue number | 4 |

Publication status | Published - Apr 2017 |

### Keywords

- Riesz spaces
- Tychonoff's Theorem
- Group Actions
- Bounded Linear Functions