Abstract and Applied Analysis
Volume 2005 (2005), Issue 3, Pages 287-305
doi:10.1155/AAA.2005.287
σ-porosity in monotonic analysis with applications to optimization
School of Information Technology and Mathematical Sciences (SITMS), Centre for Informatics and Applied Optimization, University of Ballarat, Ballarat Victoria 3353, Australia
Received 14 November 2003
Copyright © 2005 A. M. Rubinov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We introduce and study some metric spaces of increasing positively
homogeneous (IPH) functions, decreasing functions, and conormal
(upward) sets. We prove that the complements of the subset of
strictly increasing IPH functions, of the subset of strictly
decreasing functions, and of the subset of strictly conormal sets
are σ-porous in corresponding spaces. Some applications to
optimization are given.