Abstract and Applied Analysis
Volume 2005 (2005), Issue 3, Pages 287-305

σ-porosity in monotonic analysis with applications to optimization

A. M. Rubinov

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.


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.