Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions

Gianni Bosi; Alessandro Caterino; Rita Ceppitelli

doi:10.2478/v10127-010-0015-8

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Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions

Tatra Mountains Mathematical Publications

Volume 46 (2010): Issue 1 (August 2010)

By: Gianni Bosi, Alessandro Caterino and Rita Ceppitelli

Open Access

|Nov 2012

Abstract

We present new sufficient conditions for the existence of a continuous utility function for an arbitrary binary relation on a topological space. Such conditions are basically obtained by using both the concept of a weakly continuous binary relation on a topological space and the concept of a network weight. We are concerning with suitable topological notions which generalize the concept of compactness and do not imply second countability or local compactness.

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Articles in this issue

DOI: https://doi.org/10.2478/v10127-010-0015-8 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

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Language: English

Page range: 15 - 27

Published on: Nov 13, 2012

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

hereditarily Lindel¨of space,

weakly continuous binary relation,

countable network weight,

Related subjects:

© 2012 Gianni Bosi, Alessandro Caterino, Rita Ceppitelli, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Volume 46 (2010): Issue 1 (August 2010)