<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

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

Dipartimento di Matematica Applicata “Bruno de Finetti”, Universit`a di Trieste Piazzale Europa 1 I–34127 Trieste ITALY

Dipartimento di Matematica ed Informatica Universit`a di Perugia Via Vanvitelli 1 I–06123 Perugia ITALY

Tatra Mountains Mathematical Publications

We present new sufficient conditions for the existence of a continuous utility function for an arbitrary binary relation on a topological space. Such...

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

Published Online: Nov 13, 2012

Page range: 15 - 27

DOI: https://doi.org/10.2478/v10127-010-0015-8

Keywords
hereditarily Lindel¨of space, weakly continuous binary relation, countable network weight, hemicompactness, submetrizability.

This content is open access.

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

Published Online: Nov 13, 2012

Page range: 15 - 27

DOI: https://doi.org/10.2478/v10127-010-0015-8

Keywordshereditarily Lindel¨of space, weakly continuous binary relation, countable network weight, hemicompactness, submetrizability.

This content is open access.

Keywords
hereditarily Lindel¨of space, weakly continuous binary relation, countable network weight, hemicompactness, submetrizability.