Table of Contents
ISRN Applied Mathematics
Volume 2012, Article ID 240315, 23 pages
http://dx.doi.org/10.5402/2012/240315
Research Article

Near Approximations in 𝐺 π‘š -Closure Spaces

1Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
2Department of Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta 31111, Egypt
3Department of Mathematics, Faculty of Education Ibn-Al-Haitham, Baghdad University, Baghdad 4150, Iraq

Received 21 December 2011; Accepted 8 February 2012

Academic Editors: I. Doltsinis and H.-T. Hu

Copyright © 2012 M. E. Abd El-Monsef et al. 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

Most real-life situations need some sort of approximation to fit mathematical models. The beauty of using topology in approximation is achieved via obtaining approximation for qualitative subgraphs without coding or using assumption. The aim of this paper is to apply near concepts in the 𝐺 π‘š -closure approximation spaces. The basic notions of near approximations are introduced and sufficiently illustrated. Near approximations are considered as mathematical tools to modify the approximations of graphs. Moreover, proved results, examples, and counterexamples are provided.