On Continuity of Soft Mappings

2021

Journal of Mathematics

In this paper, we contribute to infrasoft topology which is one of the recent generalizations of soft topology. Firstly, we redefine the concept of soft mappings to be convenient for studying the topological concepts and notions in different soft structures. Then, we introduce the concepts of open, closed, and homeomorphism mappings in the content of infrasoft topology. We establish main properties and investigate the transmission of these concepts between infrasoft topology and its parametric infratopologies. Finally, we define a quotient infrasoft topology and infrasoft quotient mappings and study their main properties with the aid of illustrative examples.

Section: Introductionmentioning

confidence: 99%

Homeomorphism and Quotient Mappings in Infrasoft Topological Spaces

2021

Journal of Mathematics

“…This path of study began in 2011, by Shabir and Naz [27]. Since that, many papers concerning soft topologies have been published (see, for example [9,12,26,31]).…”

Section: Introductionmentioning

confidence: 99%

Soft maps via soft somewhere dense sets

Alshammari

Asaad

2020

Filomat

The concept of soft sets was proposed as an effective tool to deal with uncertainty and vagueness. Topologists employed this concept to define and study soft topological spaces. In this paper, we introduce the concepts of soft SD-continuous, soft SD-open, soft SD-closed and soft SD-homeomorphism maps by using soft somewhere dense and soft cs-dense sets. We characterize them and discuss their main properties with the help of examples. In particular, we investigate under what conditions the restriction of soft SD-continuous, soft SD-open and soft SD-closed maps are respectively soft SD-continuous, soft SD-open and soft SD-closed maps. We logically explain the reasons of adding the null and absolute soft sets to the definitions of soft SD-continuous and soft SD-closed maps, respectively, and removing the null soft set from the definition of a soft SD-open map.

“…One of the significant ideas that helps to prove some properties and removes some problems on soft topology is the concept of a soft point. It was first defined by Zorlutuna and Çakir [29] in order to study the interior points of a soft set and soft neighborhood systems. Then, [19,30] simultaneously redefined soft points to discuss soft metric spaces.…”

Section: Introductionmentioning

confidence: 99%

Soft Separation Axioms and Fixed Soft Points Using Soft Semiopen Sets

Journal of Applied Mathematics

2020

The importance of soft separation axioms comes from their vital role in classifications of soft spaces, and their interesting properties are studied. This article is devoted to introducing the concepts of t t -soft semi- T i i = 0 , 1 , 2 , 3 , 4 and t t -soft semiregular spaces with respect to ordinary points. We formulate them by utilizing the relations of total belong and total nonbelong. The advantages behind using these relations are, first, generalization of existing comparable properties on general topology and, second, eliminating the stability shape of soft open and closed subsets of soft semiregular spaces. By some examples, we show the relationships between them as well as with soft semi- T i i = 0 , 1 , 2 , 3 , 4 and soft semiregular spaces. Also, we explore under what conditions they are kept between soft topology and its parametric topologies. We characterize a t t -soft semiregular space and demonstrate that it guarantees the equivalence of t t -soft semi- T i i = 0 , 1 , 2 . Further, we investigate some interrelations of them and some soft topological notions such as soft compactness, product soft spaces, and sum of soft topological spaces. Finally, we define a concept of semifixed soft point and study its main properties.