Copyright © 2012 Samer Al Ghour and Salti Samarah. 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

Compact subsets of a topological space are used to define coc-open sets as new generalized open sets, and then coc-open sets are used to define (coc)^∗-open sets as another type of generalized open sets. Several results and examples related to them are obtained; particularly a decomposition of open sets is given. Also, coc-open sets and (coc)^∗-open sets are used to introduce coc-continuity and (coc)^∗-continuity, respectively. As a main result, a decomposition theorem of continuity is obtained.