Let X be a submetrizable k_w-space, that is the inclusive inductive limit of a decreasing sequence of second countable and locally compact subspaces of X. It is well known that X is a quotient space of a locally compact second countable space. These spaces seem to be very interesting in the study of the utility representation problem. A continuous representation theorem of Back gives the existence of a continuous map from the space of total preorders topologized by the closed convergence to the space of the utility functions endowed with a generalization of the compact-open topology. The commodity space is locally compact and second countable. Here, Back's Theorem is generalized to non-metrizable commodity spaces, precisely, to a regular space submetrizable by a boundedly compact metric or to submetrizable k_w-space.
Jointly continuous utility functions defined on submetrizable k_omega-spaces
CEPPITELLI, Rita
2012
Abstract
Let X be a submetrizable k_w-space, that is the inclusive inductive limit of a decreasing sequence of second countable and locally compact subspaces of X. It is well known that X is a quotient space of a locally compact second countable space. These spaces seem to be very interesting in the study of the utility representation problem. A continuous representation theorem of Back gives the existence of a continuous map from the space of total preorders topologized by the closed convergence to the space of the utility functions endowed with a generalization of the compact-open topology. The commodity space is locally compact and second countable. Here, Back's Theorem is generalized to non-metrizable commodity spaces, precisely, to a regular space submetrizable by a boundedly compact metric or to submetrizable k_w-space.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
