A Comparison of Different Compactness Notions in Fuzzy Topological Spaces
A Comparison of Different Compactness Notions in Fuzzy Topological Spaces
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DOI：
10.1016/0022-247x(78)90052-5
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发表时间：
1978-06
影响因子：
1.3
通讯作者：
R. Lowen
中科院分区：
文献类型：
--
作者：
R. Lowen
在本文中，我们研究了到目前为止所引入的各种紧性概念。我们将自己限制在[4]中定义的模糊拓扑空间中。在第1节中，我们给出了一些不同的特征。对于模糊紧性的一个好的定义，我们将要求在拓扑空间的特殊情况下，它与通常的紧性概念一致。在第2节中，我们将说明哪些紧性概念是好的扩展，哪些不是。此外，我们希望拓扑空间紧性的基本性质，即积的Tychonoff定理，在更一般的模糊拓扑空间中得到满足。在第三节中，我们将看到哪些概念有一个乘积定理。在第四节中，我们研究存在于不同概念之间的含义，在第五节中，我们给出一些结论。
In this paper we study the different kinds of compactness notions that have been introduced up to this time. We restrict ourselves to fuzzy topological spaces as defined in [4]. In Section 1 we give some alternative characterizations. For a good definition of fuzzy compactness we will demand that in the special case of topological spaces it coincides with the usual notion of compactness. In Section 2 we show which compactness notions are good extensions and which are not. Moreover, we want the fundamental property of compactness in topological spaces, namely, the Tychonoff theorem on products, to be fulfilled in the more general setting of fuzzy topological spaces. In Section 3 we see for which notions there is a. product theorem. In Section 4 we study the implications that exist between the different notions, and in Section 5 we give some concluding remarks.