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      • 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.

      • SCOPUSKCI등재

        Corrigendum to "On Soft Topological Space via Semi-open and Semi-closed Soft Sets, Kyungpook Mathematical Journal, 54(2014), 221-236"

        Al-shami, Tareq Mohammed Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.3

        In this manuscript, we show that the equality relations of the two assertions (ix) and (x) of [Theorem 2.11, p.p.224] in [3] do not hold in general, by giving a concrete example. Also, we illustrate that Example 6.3, Example 6.7, Example 6.11, Example 6.15 and Example 6.20 do not satisfy a soft semi $T_0$-space, a soft semi $T_1$-space, a soft semi $T_2$-space, a soft semi $T_3$-space and a soft semi $T_4$-space, respectively. Moreover, we point out that the three results obtained in [3] which related to soft subspaces are false, by presenting two examples. Finally, we construct an example to illuminate that Theorem 6.18 and Remark 6.21 made in [3] are not valid in general.

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