Existence of continuous utility functions for arbitrary binary relations: some sufficient conditions
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.
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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PDFDOI: https://doi.org/10.2478/tatra.v46i0.88