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Two notes on ``On soft Hausdorff spaces"
M. E. El-Shafei,M. Abo-Elhamayel,T. M. Al-shami 원광대학교 기초자연과학연구소 2018 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.16 No.3
One of the well known results in general topology says that every compact subset of a Hausdorff space is closed. This result in soft topology is not true in general as demonstrated throughout this note. We begin this investigation by showing that [Theorem 3.34, p.p.23] which proposed by Varol and Ayg\"{u}n [7] is invalid in general, by giving a counterexample. Then we derive under what condition this result can be generalized in soft topology. Finally, we evidence that [Example 3.22, p.p. 20] which introduced in [7] is false, and we make a correction for this example to satisfy a condition of soft Hausdorffness.
RS-Compactness in L-fuzzy Topological Spaces
M. E. EL-Shafei,I. M. Hanafy,A. I. Aggour 경북대학교 자연과학대학 수학과 2002 Kyungpook mathematical journal Vol.42 No.2
The concept of RS-compactness is introduced and studied in L-fts's. We give some characterizations of RS-compactness in terms of regular closed, semiopen and β-open L-fuzzy sets. We also characterize RS-compactness in the sense of convergent prefilterbasis and by means of finite intersection property. We investigate the image and the inverse image of RS-compact spaces under some types of functions.
Some Applications of Generalized Closed Sets in Fuzzy Topological Spaces
El-Shafei, M.E. Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.1
In this paper we introduce the notions of g-regularity and g-normality in fuzzy topological spaces. We obtain some characterizations and several preservation theorems of such spaces.
On soft compact and soft Lindel\"{o}f spaces via soft pre-open sets
T. M. Al-shami,M. E. El-Shafei 원광대학교 기초자연과학연구소 2019 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.17 No.1
In this study, the authors employ soft pre-open sets to define and discuss eight sorts of generalized soft compact spaces, namely soft pre-compact, soft pre-Lindel\"{o}f, almost (approximately, mildly) soft pre-compact and almost (approximately, mildly) soft pre-Lindel\"{o}f spaces. Then they characterize each one of these spaces and show the relationships among them with the help of examples. Also, they investigate the image of these spaces under soft pre-irresolute mappings. Furthermore, they present a soft pre-partition notion and point out this notion is sufficient for the equivalent among the four types of soft pre-compact spaces and for the equivalent among the four types of soft pre-Lindel\"{o}f spaces. They demonstrate the relationships between enriched soft topological spaces and the initiated spaces in different cases and obtain interesting results. Finally, they derive some findings which connect between some generalized soft compact spaces introduced in this work and some soft topological notions such as soft pre-connected spaces, soft pre-$T_2$-spaces and soft subspaces.
The ring of soft pˆ-adic numbers
Fawzan Sidky,M. E. El-Shafei,M. K. Tahat 원광대학교 기초자연과학연구소 2021 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.21 No.2
We have studied and investigated the soft integers as a significant subset of soft real numbers, as we have developed many well-known theorems over integers to deal with the soft theory like the Chinese remainder theorem over the soft integers beside many other theories. Also, we have studied and investigated the p-adic numbers in the aspect of the soft theory to introduce the ring of soft pˆ-adic numbers and study some of their properties.
Fawzan Sidky,M. E. El-Shafei,M. K. Tahat 원광대학교 기초자연과학연구소 2021 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.21 No.3
In this paper, we have introduced the concept of the soft topological module over soft topological rings as a hybrid of algebraic and soft topological structures. Also, we have studied the properties of soft topological module and their subsystem.
Fawzan Sidky,M. E. El-Shafei,M. K. Tahat 원광대학교 기초자연과학연구소 2020 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.20 No.3
In this paper, we have proposed a refinement for the concept of soft mapping along with a new definition of the soft element of soft sets to discuss the soft continuity of soft mapping over soft sets. Moreover, we have introduced the concept of soft modules over soft rings and studied the soft continuity of soft module operations over soft topological spaces to proceed with the main goal of this paper. Introducing the concept of soft topological soft modules.