Related papers: Methods of generating soft topologies and soft sep…
In the study of soft topological spaces, two types of separation axioms have given if soft points and single point soft sets have been taken as separated objects respectively. In this paper, some examples and properties are given to explore…
Concept of bi-soft topological spaces is introduced. Several notions of a soft topological space are generalized to study bi-soft topological spaces. Separation axioms play a vital role in study of topological spaces. These concepts have…
We present a construction of the soft $T_{0}$ reflection of a soft topological space and characterize some separation axioms developed through the soft $T_{0}$ reflection.
Working in the soft-element (classical) viewpoint, we introduce \emph{soft bitopological groups}: soft groups endowed with two soft topologies such that the induced topologies on the set of soft elements make the soft-element group into a…
We introduce soft bitopological spaces from the standpoint of soft elements. A soft bitopological space is a soft set equipped with two soft topologies. Following the classical construction of Goldar--Ray, each soft topology on $F$ induces…
The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft…
The cluster soft point is an attempt to introduce a novel generalization of the soft closure point and the soft limit point. A cluster soft set is defined to be the system of all cluster soft points of a soft set. Then the fundamental…
Topological mechanics can realize soft modes in mechanical metamaterials in which the number of degrees of freedom for particle motion is finely balanced by the constraints provided by interparticle interactions. However, solid objects are…
In this study, the soft usual topology compatible with the usual topology of $\mathbb{R}$ is defined, and using its subspace topology on the interval $[0,1]$, the concept of a soft path is introduced. Within this context, the notions of…
Soft uniform structures provide a way to speak about uniform closeness in a parameterized setting. Working over a fixed parameter set, we treat entourages as soft relations and introduce a notion of \emph{soft uniformity} whose axioms…
In various articles, it is said that the class of all soft topologies on a common universe forms a complete lattice, but in this paper, we prove that it is a complete lattice. Some soft topologies are maximal and some are minimal with…
We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…
Double-soft theorems, like its single-soft counterparts, arises from the underlying symmetry principles that constrain the interactions of massless particles. While single soft theorems can be derived in a non-perturbative fashion by…
The purpose of this paper is to construct topology on vague soft sets. The concept of vague soft topology is introduced and its basic properties are given.
We introduce the concept of a soft ditopological space as the "soft generalization" of the concept of a ditopological space as it is defined in the papers by L.M. Brown and co-authors, see e.g. L. M. Brown, R. Erturk, S. Dost,…
The soft topological spaces and some their related concepts have stud- ied in [7]. In this paper, we introduce and study the notions of soft connected topological spaces after a review of preliminary definitions.
Basic pairs and their morphisms are the most elementary framework in which standard topological notions can be defined. We present here a new interpretation of topological concepts as those which can be communicated faithfully between the…
This paper introduces semiopen and semiclosed soft sets in soft topological spaces. The notions of interior and closure are generalized using these sets. A detail study is carried out on properties of semiopen, semiclosed soft sets, semi…
In this paper we give a new definition of soft topology using elementary union and elementary intersection although these operations are not distributive. Also we have shown that this soft topology is different from Naz's soft topology and…
Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative…