Cocompact Open Sets and Continuity

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.