L-Fuzzy Semi-Preopen Operator in L-Fuzzy Topological Spaces

In this paper, we give the concept of L-fuzzy Semi-Preopen operator in L-fuzzy topological spaces, and use them to score L-fuzzy SP-cmpactnness in L-fuzzy topological spaces. We also study the relationship between L-fuzzy SP-compactness and SP-compactness in L-topological spaces

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

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

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

Survey on preopen sets

The aim of this survey article is to cover most of the recent research on preopen sets. I try to present majority of the results on preopen sets that I am aware of.Comment: To appear in the Proceedings of the 1998 Yatsushiro Topological Conference, 22-23 August 199

An Embedding Lemma in Soft Topological Spaces

In 1999, Molodtsov initiated the concept of Soft Sets Theory as a new mathematical tool and a completely different approach for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the theory 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 for soft topological spaces

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

pp-adic discrete dynamical systems and their applications in physics and cognitive sciences

This review is devoted to dynamical systems in fields of $p$-adic numbers: origin of $p$-adic dynamics in $p$-adic theoretical physics (string theory, quantum mechanics and field theory, spin glasses), continuous dynamical systems and discrete dynamical systems. The main attention is paid to discrete dynamical systems - iterations of maps in the field of $p$-adic numbers (or their algebraic extensions): conjugate maps, ergodicity, random dynamical systems, behaviour of cycles, holomorphic dynamics. dynamical systems in finite fields. We also discuss applications of $p$-adic discrete dynamical systems to cognitive sciences and psychology

Fixed point theorems of soft contractive mappings

The first aim of this paper is to examine some important properties of soft metric spaces. Second is to introduce soft continuous mappings and investigate properties of soft continuous mappings. Third is to prove some fixed point theorems of soft contractive mappings on soft metric spaces.Comment: arXiv admin note: text overlap with arXiv:1308.3390; and text overlap with arXiv:1305.4545 by other author

Topological systems as a framework for institutions

Recently, J.~T.~Denniston, A.~Melton, and S.~E.~Rodabaugh introduced a lattice-valued analogue of the concept of institution of J.~A.~Goguen and R.~M.~Burstall, comparing it, moreover, with the (lattice-valued version of the) notion of topological system of S.~Vickers. In this paper, we show that a suitable generalization of topological systems provides a convenient framework for doing certain kinds of (lattice-valued) institutions