Applications of utility functions defined on quasi-metric spaces
by
Manuel Sanchis
Departament de Matemàttiques, Universitat Jaume I (Spain)
Coauthors: S. Romaguera

Motivated, in part, by some problems from mathematical economics, Levin characterized in [1] preferences on a separable metric spaces that admit Lipschitz utility functions. He also used this type of functions, and other related ones, to the study of choice functions and discrete dynamical systems. In this talk we show that the concepts of preference and of utility function also constitute tools to explain the properties of many kinds of spaces which naturally arise in theoretical computer science; in particular, in domain theory [2] and complexity theory [3]. Since such spaces are quasimetrizable but nonmetrizable, we develop our theory in the realm of quasimetric spaces.

Reference

[1] V.L. Levin, Some applications of set-valued mappings in mathematical economics, J. Math. Econom. 20 (1991) 69-87.

[2] S.G. Mathews, Partial metrixc topology, in: Proc. 8th Summer Conference on General Topology and Appl. Ann. New York Acad. Sci. 728 (1994) 183-197.

[3] M. Schellekens, The Smyth completion: a common foundation for denotational semantics and complexity analysis, in Proc. MFPS 11, Electron. Notes Theor. Comput. Sci. 1 (1995) 211-232.

Date received: May 15, 2003