Abstract
In the article first we introduce a new notion of soft element of a soft set and establish its natural relation with soft operations and soft objects in soft topological spaces. Next, using the notion of soft element, we define, in a different way than in the literature, a soft mapping transforming a soft set into a soft set and provide basic properties of such mappings. The new approach to soft mappings enables us to obtain the natural first fixed-point results in the soft set theory. Throughout the paper a comprehensive set of examples illustrating the discussed topics is presented. MSC:47H10, 54A05.
Highlights
The soft set theory, initiated by Molodtsov [ ] in, is one of the branches of mathematics, which aims to describe phenomena and concepts of an ambiguous, undefined, vague and imprecise meaning
The interesting paper is [ ], where the authors introduced the notion of soft topology on a soft set and proved basic properties concerning soft topological spaces
4 Soft compact topological spaces we introduce the definitions and the basic properties concerning soft compact topological spaces, which will be useful
Summary
The soft set theory, initiated by Molodtsov [ ] in , is one of the branches of mathematics, which aims to describe phenomena and concepts of an ambiguous, undefined, vague and imprecise meaning. Using the introduced notion of soft element, the following proposition gives a natural characterization of soft open sets. A soft relation T ⊆ ̃ F × ̃ G is called a soft mapping from F to G, which is denoted by T : F → ̃ G, if the following two conditions are satisfied:. The inverse of Y ⊆ ̃ G under soft mapping T is the soft set, denoted by T– (Y ), of the form. Let (K, τ) be a soft compact topological space and let T : K → ̃ K be a soft continuous mapping. Proof Let {Vi}i∈I ⊆ τbe such that T(K ) ⊆ ̃ ̃ i∈IVi. Due to the soft continuity of T , we get that {T– (Vi)}i∈I is a family of soft open sets.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
