The aim of this research is to use the class of soft simply open set to define new types of separation axioms in soft topological spaces. We also introduce and study the concept of soft simply compactness.

        In this paper, we introduce the notation of the soft bornological group to solve the problem of boundedness for the soft group. We combine soft set theory with bornology space to produce a new structure which is called    soft bornological group. So that both the product and inverse maps are soft bounded. As well as, we study the actions of the soft bornological group on the soft bornological sets. The aim soft bornological set is to partition into orbital classes by acting soft bornological group on the soft bornological set. In addition, we explain the centralizer, normalizer, and stabilizer in details. The main important results are to prove that the product of soft bornological groups is soft bornol

      In this work, we introduced and studied  a new kind of soft mapping  on soft topological spaces with an ideal, which we called  soft strongly generalized mapping with respect an ideal I, we studied the concepts like SSIg-continuous, Contra-SSIg-continuous, SSIg-open, SSIg-closed and SSIg-irresolute mapping  and  the relations between these kinds of mappings and the composition of two mappings of the same type of two different types, with proofs or counter examples

In this paper we define a signal soft set as a mathematical tool to represent and study atoms, anti-atoms, electrons, anti-electrons, protons, and anti-protons, and generate a signal soft topology, with an example of signal soft topology on H₂O.

In this paper, the C̆ech fuzzy soft closure spaces are defined and their basic properties are studied. Closed (respectively, open) fuzzy soft sets is defined in C̆ech fuzzy-soft closure spaces. It has been shown that for each C̆ech fuzzy soft closure space there is an associated fuzzy soft topological space. In addition, the concepts of a subspace and a sum are defined in C̆ech fuzzy soft closure space. Finally, fuzzy soft continuous (respectively, open and closed) mapping between C̆ech fuzzy soft closure spaces are introduced. Mathematics Subject Classification: 54A40, 54B05, 54C05.

      In this paper, we  introduce new concepts that relates to soft space based on   work that was previously presented by researchers in this regard. First we give  the definition of Soft Contraction Operator and some examples. After that we introduce the concepts of soft Picard iteration and soft Mann iteration processes. We also give  some examples to illustrate them.

    Many concepts in normed spaces have been generalized in soft normed spaces. One of the important concepts is the concept of stability of soft iteration in soft normed spaces. We discuss this concept by giving some lemmas that  are  used to prove some theorems about stability of soft i

Let
be an
module, and let
be a set, let
be a soft set over
. Then
is said to be a fuzzy soft module over
iff
,
is a fuzzy submodule of
. In this paper, we introduce the concept of fuzzy soft modules over fuzzy soft rings and some of its properties and we define the concepts of quotient module, product and coproduct operations in the category of
modules.