Open questions in utility theory

Throughout this paper, our main idea is to explore different classical questions arising in Utility Theory, with a particular attention to those that lean on numerical representations of preference orderings. We intend to present a survey of open questions in that discipline, also showing the state-of-art of the corresponding literature.This work is partially supported by the research projects ECO2015-65031-R, MTM2015-63608-P (MINECO/ AEI-FEDER, UE), and TIN2016-77356-P (MINECO/ AEI-FEDER, UE)

Normally preordered spaces and utilities

In applications it is useful to know whether a topological preordered space is normally preordered. It is proved that every $k_\omega$-space equipped with a closed preorder is a normally preordered space. Furthermore, it is proved that second countable regularly preordered spaces are perfectly normally preordered and admit a countable utility representation.Comment: 17 pages, 1 figure. v2 contains a second proof to the main theorem with respect to the published version. The last section of v1 is not present in v2. It will be included in a different wor