### Abstract

.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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### Cite this

}

*Asian Journal of Mathematics and Computer Research*, vol. 7, no. 4, pp. 206-211.

**Group Invariant Bounded Linear Functions on Dedekind Complete Totally Ordered Riesz Spaces.** / Chailos, George.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Group Invariant Bounded Linear Functions on Dedekind Complete Totally Ordered Riesz Spaces

AU - Chailos, George

PY - 2017/4

Y1 - 2017/4

N2 - 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.

AB - 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.

KW - Riesz spaces

KW - Tychonoff's Theorem

KW - Group Actions

KW - Bounded Linear Functions

M3 - Article

VL - 7

SP - 206

EP - 211

JO - Asian Journal of Mathematics and Computer Research

JF - Asian Journal of Mathematics and Computer Research

SN - 2395-4205

IS - 4

ER -