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Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 54027, 14 pages
doi:10.1155/JIA/2006/54027

A generic result in vector optimization

Alexander J. Zaslavski

Department of Mathematics, The Technion-Israel Institute of Technology, Haifa 32000, Israel

Received 17 November 2005; Revised 19 March 2006; Accepted 24 March 2006

Abstract

We study a class of vector minimization problems on a complete metric space such that all its bounded closed subsets are compact. We show that for most (in the sense of Baire category) problems in the class the sets of minimal values are infinite.