الفهرس 
PreliminariesOnly 14 pages are availabe for public view
 |  | from | 119 |  |  |
| | | from | 119 | | |
Abstract
This thesis consists of five chapters distributed as follows:
Chapter 1: is the introductory chapter, so it contains the basic concepts and
properties of set theory and mset theory. It contains also the basic concepts
and properties of topological space such as closure, interior, boundary, functions,
separation axioms. The basic concepts and properties of bitopological spaces are
presented. Further, this chapter contains the basic notions related to soft sets
and soft topological spaces. Additionally, in Subsection 1.6, the concept of soft
msets is introduced by Tokat et al. [65]. Moreover, the soft multi function and
it’s properties are introduced in this subsection.
In Chapter 2, the concept of supra M-topological spaces is introduced initially.
Then, the notions of supra -operation, supra pre-open msets, supra _-open msets,
supra semi open msets, supra _-open msets and supra b-open msets are presented.
The properties of the present notions are studied and the relationships between
them are given. The importance of this approach is that, the class of supra M-topological spaces is wider and more general than the class of M-topological spaces.
For a special case, we introduced the notion of -operation in M-topological spaces.
The goal of Chapter 3 is to study some (soft) multi topological properties in
(soft) multi topological spaces which are represented by introducing separation
axioms on M-topological spaces and study some of their properties. In addition,
some algebraic structures on soft msets are obtained. Also, we introduced the
notion of soft multi semi-compactness as a generalization of semi-compact in M-topological spaces and study its properties. Finally, we see that Theorem 1.6.3
in [65] is not correct and that is explained by a counter example. Moreover, the
concept of semi-connectedness in soft multi topological spaces is introduced.
In Chapter 4, we introduced the concepts of generalized closed (open) soft msets
and their properties. Also, the relationship between the current work and the previous
one [39] is presented with the help of counter examples. Additionally, we
introduced the concept of separated soft msets in soft multi topological spaces
and study some results about this concept. The main purpose of Subsection 4.2 is
to introduce the notions of -operation, pre-open soft msets, _-open msets, semiopen
soft msets, _-open soft msets and b-open soft msets in soft multi topological
spaces. The current notions are a generalization of the notions in [35]. In addition,
the relationships among these types are studied. Moreover, the concepts
of pre-continuous (respectively semi-continuous, _-continuous, _-continuous, b-continuous) soft multi functions are introduced and their properties are studied
in detail. Also, the concepts of pre-irresolute (respectively semi-irresolute, _-
irresolute, _-irresolute, b-irresolute) soft multi functions are presented.
The main purpose of Chapter 5 is to introduce the notion of multiset bitopological
spaces and study some M-operators on multiset bitopological spaces. Moreover,
the notions of ij-operators such as ij-pre-open msets, ij-_-open msets,
ij-semi-open msets and ij-_-open msets are presented on multiset bitopological
spaces. The properties of these operators are studied and the relationships
between them are given. Additionally, some deviations between M-topology and
ordinary topology are given with the help of counter examples. The importance
of this approach is that, the class of multiset bitopological spaces is more general
than the class of bitopological spaces.