Soft N-Topological Spaces

Very recently, the idea of studying structures equipped with two or more soft topologies has been considered by several researchers. Soft bitopological spaces were introduced and studied, in 2014, by Ittanagi as a soft counterpart of the notion of bitopological space and, independently, in 2015, by Naz, Shabir and Ali. In 2017, Hassan too introduced the concept of soft tritopological spaces and gave some first results. The notion of N-topological space related to ordinary topological spaces was instead introduced and studied, in 2011, by Tawfiq and Majeed. In this paper we introduce the concept of Soft N-Topological Space as generalization both of the concepts of Soft Topological Space and N-Topological Space and we investigate such class of spaces and their basic properties with particular regard to their subspaces, the parameterized families of crisp topologies generated by them and some new separation axioms called N-wise soft T0, N-wise soft T1, and N-wise soft T2.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1905.1305

Parameterized Norm and Parameterized Fixed-Point Theorem by Using Fuzzy Soft Set Theory

From last decade, when Molodtsov introduced the theory of soft set as a new approach to deal with uncertainties, until now this theory was considered sharply by a fair number of researchers. Combination of fuzzy set theory and soft set theory, called fuzzy soft set theory, by Maji et.al opened a new way for researchers whose frame work of study is soft sets and fuzzy sets. Although published papers in this area have considered both application and theoretical aspects of fuzzy soft set theory, the concept of norm for a fuzzy soft set has not been studied yet. We begin this paper by introducing fuzzy soft real numbers, which are needed for study fuzzy soft norm, and then continued by considering fuzzy soft norm. Fixed-point theorem is also investigated for fuzzy soft normed spaces.Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1308.425

Semiopen and semiclosed sets in fuzzy soft topological spaces

In this paper, we introduce semiopen and semiclosed fuzzy soft sets in fuzzy soft topological spaces. Various properties of these sets are studied alongwith some characterizations. Further, we generalize the structures like interior and closure via semiopen and semiclosed fuzzy soft sets and study their various properties

A Soft Embedding Lemma for Soft Topological Spaces

In 1999, Molodtsov initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the notion of soft topological spaces, also defining and investigating many new soft properties as generalization of the classical ones. In this paper, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Lemma to the class of soft topological spaces.Comment: 23 pages. arXiv admin note: substantial text overlap with arXiv:1904.01481, arXiv:1905.1233

On Soft Mappings

In this paper, we introduce soft continuous mappings which are defined over an initial universe set with a fixed set of parameters. Later we study soft open and soft closed mappings, soft homeomorphism and investigate some properties of these concepts.Comment: 12 page

Fuzzy soft seperation axioms with sense of Ganguly and Saha

Tanay and Kandemir TK introduced the topological structure of fuzzy soft sets. In 2013, Manatha and Das md defined seperation axioms on fuzzy soft topological spaces. In this paper, we generalized form of the seperation axioms.using fuzzy soft quasi-coincidence with sense of Ganguly and Saha GS. By using this notions, we also give some basic theorems of seperation axioms in classical topological spaces

Results on fuzzy soft topological spaces

B. Tanay et. al. introduced and studied fuzzy soft topological spaces. Here we introduce fuzzy soft point and study the concept of neighborhood of a fuzzy soft point in a fuzzy soft topological space. We also study fuzzy soft closure and fuzzy soft interior. Separation axioms and connectedness are introduced and investigated for fuzzy soft topological spaces

Soft Topology on Function Spaces

Molodtsov initiated the concept of soft sets in Molodtsov D. Maji et al. defined some operations on soft sets in Maji P. K., Bismas R., Roy A. R. The concept of soft topological space was introduced by some authors. In this paper, we introduce the concept of the pointwise topology of soft topological spaces and the properties of soft mappings spaces. Finally, we investigate the relationships between some soft mappings spaces.Comment: 13 pages,Submitted a journal for publication. arXiv admin note: text overlap with arXiv:1305.4545 by other author

Some Notes on Compact Sets in Soft Metric Spaces

The first aim of this study is to define soft sequential compact metric spaces and to investigate some important theorems on soft sequential compact metric space. Second is to introduce net and totally bounded soft metric space and study properties of this space. Third is to define Lebesque number and soft uniformly continuous mapping and investigate some theorems in detail.Comment: arXiv admin note: text overlap with arXiv:1305.4545 by other author

Notes on interval-valued Hesitant fuzzy soft Topological Space

In this paper we introduce the notion of interval valued hesitant fuzzy soft topological space. Also the concepts of interval valued hesitant fuzzy soft closure, interior and neighbourhood are introduced here and established some important results.Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1604.0090