Utility Theory without the Completeness Axiom - Aumann, Robert J. (Econometrica, 1962)
Some theorems concerning the existence of continuous utility functions for closed preorders on submetrizable hemicompact kspaces are proved.These spaces are precisely the inductive limits of increasing sequences of metric compact subspaces and in general are neither metrizable nor locally compact.These results generalize some well known theorems due to Levin.