The problem of the existence of jointly continuous utility functions is studied. A continuous representation theorem of Back [1] gives the existence of a continuous map from the space of total preorders topologized by closed convergence (Fell topology)to the space of utility functions with different choice sets (partial maps)endowed with a generalization of the compact-open topology.The commodity space is locally compact and second countable. Our results generalize Back’s Theorem to non-metrizable commodity spaces with a family of not necessarily total preorders. Precisely, we consider regular commodity spaces having a weaker locally compact second countable topology.
Some generalizations of Back's Theorem
CATERINO, Alessandro;CEPPITELLI, Rita;
2013
Abstract
The problem of the existence of jointly continuous utility functions is studied. A continuous representation theorem of Back [1] gives the existence of a continuous map from the space of total preorders topologized by closed convergence (Fell topology)to the space of utility functions with different choice sets (partial maps)endowed with a generalization of the compact-open topology.The commodity space is locally compact and second countable. Our results generalize Back’s Theorem to non-metrizable commodity spaces with a family of not necessarily total preorders. Precisely, we consider regular commodity spaces having a weaker locally compact second countable topology.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.