Decomposition of some kinds of mixed multiset continuity on multiset topological spaces

Abstract

Recently, El-Sharkasy et al., El-Sharkasy and Badr have shown that to find the mutations of deoxyribonucleic acid (DNA) and ribonucleic acid (RNA), multiset topology is very much essential. In this article we give the definitions of mixed (1,2)-pre-open (resp. mixed (1,2)-semi-open, mixed (1,2)-α-open, mixed (1,2)β-open) mset via two multiset topologies. Besides, we procure the notions of mixed (1,2)-pre (resp. mixed (1,2)-semi, mixed (1,2)α, mixed (1,2)-β) mset continuity between two M-topological spaces (M,τ 1), (M,τ 2) and an M-topological space (N,σ). A decomposition of these types is investigated. Finally, we prove that every τ 1 -mset continuous function is mixed (1,2)-pre- (resp. mixed (1,2)semi-, mixed (1,2)-α-, mixed (1,2)-β-) mset continuous function. MSC Classification: 03E70 , 54C05 , 54C08