Open AccessContinuous representability of complete preorders on the space of upper-continuous capacities
Author(s) -
Gianni Bosi,
Romano Isler
Publication year - 2001
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2001.3012
Subject(s) - preorder , mathematics , metric space , space (punctuation) , continuous function (set theory) , topology (electrical circuits) , continuous functions on a compact hausdorff space , complete metric space , pure mathematics , function (biology) , compact space , discrete mathematics , locally compact space , metric (unit) , algebra over a field , combinatorics , computer science , evolutionary biology , biology , operations management , economics , operating system
Given a compact metric space (X, d), and its Borel σ-algebra Σ, we discuss the existence of a (semi)continuous utility function U for a complete preorder ≤ on a subset M’(X) of the space M(X) of all upper-continuous capacities on Σ, endowed with the weak topology