A Study of Downward Sets with p-Functions |
| |
| Authors: | H Mohebi V Momenaei Kermani |
| |
| Institution: | 1. Mahani Mathematical Research Center, and Department of Mathematics , Shahid Bahonar University of Kerman , Kerman, Iran hmohebi@mail.uk.ac.ir;3. Islamic Azad University, Kerman Branch , Kerman, Iran |
| |
| Abstract: | In this paper, we study downward sets and increasing functions in a topological vector space and their similarities to the convex sets and convex functions. It will be shown that a very special increasing function, namely, the p-function, can give a geometric interpretation for separating downward sets from outside points. Also, this function can be used to approximate topical functions in the framework of abstract convexity. |
| |
| Keywords: | Abstract convexity Downward set Monotonic analysis p-function Topical function |
|
|
