On the structure of completely useful topologies | Zendy

Gianni Bosi | Zendy; Gerhard Herden | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

On 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

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research