Open AccessOn the structure of completely useful topologies
Author(s) -
Gianni Bosi,
Gerhard Herden
Publication year - 2002
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2002.2060
Subject(s) - span (engineering) , mathematics , axiom , combinatorics , function (biology) , topology (electrical circuits) , discrete mathematics , geometry , structural engineering , evolutionary biology , engineering , biology
Let X be an arbitrary set. Then a topology t on X is completely useful if every upper semicontinuous linear preorder on X can be represented by an upper semicontinuous order preserving real-valued function. In this paper we characterize in ZFC (Zermelo-Fraenkel + Axiom of Choice) and ZFC+SH (ZFC + Souslin Hypothesis) completely useful topologies on X. This means, in the terminology of mathematical utility theory, that we clarify the topological structure of any type of semicontinuous utility representation problem