ON DIFFERENCE OPEN MULTISETS IN M-TOPOLOGICAL SPACES

unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract. In this paper, we introduce and study some of the topological properties of oD-mset, o−∆ mset by using the concept of open msets. Also, we present new separation axioms by using the notions of open msets, oD-mset, o−∆ mset, pre-open mset and semi-open mset and study some of its properties.


INTRODUCTION
N. Levine [11] introduced the notation of semi open sets in a topological space. In 1997,Caldas [3] defined a semi-Difference (briefly sD) sets and semi-D i spaces for i = 0, 1, 2. Ashish Kar and Bhattacharya [10], in 1990, also defined pre-T i spaces for i = 0, 1, 2. Another set of separation axioms analogous to the semi separation axioms defined in [13]. A set is a collection of distinct objects "well define". If there is a repetition in the items, this set is called multiset (mset, for short), is obtained [2,15]. For the sake of convenience a mset is write as {n 1 /y 1 , n 2 /y 2 , ..., n l /y l } the element y i occurs n i times. n i is a positive integer. Multiset have many uses, including the expression of gene sequences for DNA, as well as the study of mutations [4,5], and in the near future it will be of great importance in a study in next generation of sequence.Defining new sets of multiset and defining the separation axioms on them will help in the future in studying the repair of mutations, and this is what we are working on studying in future work.
In this research, we introduce and study topological properties of oD-multiset, o − ∆ multiset by using the concept of open msets. We also present and study new separation axioms by using the notions of pre-open multiset,semi-open multiset, oD-multiset, o − ∆ multiset.

PRELIMINARIES
In this section, a brief survey of some basic concepts of multiset, separation axioms on multiset topology and separation axioms. Definition 2.1 (9). Let Y be a support set and [Y ] n be the multiset space defined over Y . For any muliset This is useful in changing the nature or sequence of the chromosome to avoid the emergence of diseases and the occurrence Mutation.
Sobhy El-Sheikh and et. al [7] introduced a whole M-singleton and M − T i spaces for i = 0, 1, 2, 3, 4, 5. They study the relation between M − T i spaces.
Caldas [3] defined a semi-Difference sets (briefly sD) by semi-open sets [11], and introduced the semi-D i spaces for i = 0, 1, 2. and open-D i spaces for i = 0, 1, 2, as in [1] and study the relation between them.
Theorem 2.5. For a space (Y, τ) the following are true: Monsef [1] defined an open-symmetric difference (o∆) sets [1] by using the open sets, and introduced the o − ∆ i spaces for i = 0, 1, 2, as in [1]and study the relation between them.
The notions of interior and closure of an M-set in M-topology have been introduced and studied by Jacob et al. [8]. The other topological structures like exterior and boundary have remain untouched by Mahanta and Das [12] introduce the concepts of exterior and boundary in multiset topology. Consider an M-topological space El-Sheikh et al. [6] defined submsets of M-topological spaces.

SEPARATION AXIOMS
there is a semi-open mset containing one of the M-singletons but not the other.
It is clear that when the disease appears in the chromosome and we wanted this part of the patient and eliminate the right for the part and it is using the group and this gives a higher resolution if the injury at one end of chromosome.       (2) Every M − T i ,space is M − oD i space, i = 0; 1; 2.

OPEN-SYMMETRIC DIFFERENCE MSET
We defined an open-symmetric difference msets ( o∆-mset) by using the open msets, and defined the the M − o∆ i spaces for i = 0, 1, 2.
Appeared many ways to separate the disease (part proper for the sick, injured or suspected of having), but was for this method many conditions which reduce the importance and when there is a way to show this chapter anywhere in the chromosome, this method is high-resolution. (2) Every M − oD i space is M − o∆ i pace, i = 1;2.

Proof. Straightforward.
We all know that mathematical applications and solving life problems are among the most important issues that all or most researchers are interested in. But this does not leave us far from the theory that we will need in the future as we are currently using the previous theories, for example the multiple group exists from 1986 [15] and it was used in many applications in different fields, but we in 2018 [4,5] used it differently to express the gene and reveal Mutations.
In this research, we worked on establishing new types of multiple groups and new separation axioms and theories on them.

CONCLUSIONS
In this paper we introduce the separation axioms on mset topological spaces and difference mset topological spaces based on the singleton mset {m/x}, oD-mset, o−∆ mset, pre-open mset and semi-open mset. In the future, we study another topological property such as connected, some types of submsets and mappings on these spaces, we will use a new separation axioms in repair mutations and treat diseases.

CONFLICT OF INTERESTS
The author(s) declare that there is no conflict of interests.