15 research outputs found
Minimal spaces with a mathematical structure
No full textAbstractThis paper will discuss, grill topological space which is not only a space for obtaining a new topology but generalized grill space also gives a new topology. This has been discussed with the help of two operators in minimal spaces
New operators in ideal topological spaces and their closure spaces
No full textIn this paper, we introduce two operators associated with ψ* and *ψ operators in ideal topological spaces and discuss the properties of these operators. We give further characterizations of Hayashi-Samuel spaces with the help of these two operators. We also give a brief discussion on homeomorphism of generalized closure spaces which were induced by these two operators
µ -k -Connectedness in GTS
No full textopen sets and µ -β -open sets in a GTS (X, µ). By using the µ -σ -closure, µ -π -closure, µ -α -closure and µ -β -closure in (X, µ), we introduce and investigate the notions µ -k -separated sets and µ -k -connected sets in (X, µ)
Algebra of frontier points via semi-kernels
No full textIn topological spaces, the study of interior and closure of a set are renowned concepts where the interior is defined as the union of open sets and the closure is defined as the intersection of closed sets. In literature, it is also a significant study while a set is defined as the intersection of open sets, and the union of closed sets. These respective ideas are known as the kernel of a set and its complementary function. Utilizing these ideas, some authors have introduced various kinds of results in topological spaces. Some mathematicians have extended these concepts via Levine’s semi-open sets to semi-kernel and its complementary function. The study of these notions is also a remarkable part of the field of topological spaces as the collection of semi-open sets does not form a topology again. In this paper, we have taken the semi-kernel and its complementary function into account to introduce new types of frontier points. After that we have studied and presented several characterizations of these new types of frontiers and established relationships among them. Finally, we have shown that semi-homeomorphic images of these new types of frontiers are invariant
Set operators and associated functions
No full textThe study of two operators local function and the set operator
ψ
on the ideal topological spaces are likely to be same to the study of closure and interior operator of the topological spaces. However, they are not exactly equal with the interior and closure operator of the topological spaces. In this context, we introduce two new set operators on the ideal topological spaces. Detail properties of these two operators are the part of this article. Furthermore, the operators interior (resp.
ψ
) and closure (local function) obey the relation
I
n
t
(
A
)
= X \
C
l
(X \ A) (resp.
ψ
(A) = X \(X \A)
∗
)
. We search the general method of these relations, through this manuscript.Trdizi
A note on mathematical structures
No full textIn this paper we shall discuss the interrelations between generalizations of topology and mathematical structures. We also discuss the algebraic nature of generalizations of topology and mathematical structures.</jats:p
TOPOLOGIES ON THE FUNCTION SPACE WITH VALUES IN A TOPOLOGICAL GROUP
No full textLet denote the set of all functions from to . When is a topological space, various topologies can be defined on . In this paper, we study these topologies within the framework of function spaces. To characterize different topologies and their properties, we employ generalized open sets in the topological space . This approach also applies to the set of all continuous functions from to , denoted by , particularly when is a topological group. In investigating various topologies on both and , the concept of limit points plays a crucial role. The notion of a topological ideal provides a useful tool for defining limit points in such spaces. Thus, we utilize topological ideals to study the properties and consequences for function spaces and topological groups
