http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
T. M. Al-shami 원광대학교 기초자연과학연구소 2018 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.15 No.3
In [7], the authors reported that a soft $T_i$-space need not be a soft $T_{i-1}$-space, for $i=3, 4, 5$ [Line 4 and 5 in abstract] and [Theorem 3.21], and the soft $T_i$-spaces in the sense of [3] and soft $T_i$-spaces in their work are equivalent, for $i=0, 1, 2, 3$ [Line 7 and 8 in abstract] and [Line 12 and 13, p.p. 522]. In this note, we correct the errors in these assertions by proving that every soft $T_3$-space is a soft $T_{2}$-space and presenting two counterexamples to show that a soft $T_i$-space in the sense of [3] is not equivalent to a soft $T_{i}$-space in the sense of [7], for $i=2, 3$.
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.
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.