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      • KCI등재후보

        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.

      • KCI등재

        Seven generalized types of soft semi-compact spaces

        Tareq Mohammed Al-shami,Mohammed E. El-Shafei,Mohammed Abo-Elhamayel 강원경기수학회 2019 한국수학논문집 Vol.27 No.3

        The soft compactness notion via soft topological spaces was first studied in [10,29]. In this work, soft semi-open sets are utilized to initiate seven new kinds of generalized soft semi-compactness, namely soft semi-Lindel\"{o}fness, almost (approximately, mildly) soft semi-compactness and almost (approximately, mildly) soft semi- Lindel\"{o}fness. The relationships among them are shown with the help of illustrative examples and the equivalent conditions of each one of them are investigated. Also, the behavior of these spaces under soft semi-irresolute maps are investigated. Furthermore, the enough conditions for the equivalence among the four sorts of soft semi-compact spaces and for the equivalence among the four sorts of soft semi-Lindel\"{o}f spaces are explored. The relationships between enriched soft topological spaces and the initiated spaces are discussed in different cases. Finally, some properties which connect some of these spaces with some soft topological notions such as soft semi-connectedness, soft semi $T_2$-spaces and soft subspaces are obtained.

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