Generating fuzzy topologies with semi-closure operators

✍ Scribed by Albert J. Klein

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 454 KB
• Volume: 9
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(83)80027-x

✦ Synopsis

Let X be an L-fuzzy topological space. For Q E L -{l} and A c X, x E c,(A) if and only if G fuzzy-open and G(x)> a imply there is (z E A with G(a) > 0. Under certain restrictions on (Y, which are always satisfied if L is linearly ordered, c, is a semi-closure operator. This paper contains necessary and sufficient conditions under which a collection of semi-closure operators generates a fuzzy topology. In general, such a collection does not generate a unique topology. The class of topologies generated is shown to be closed under suprema and its largest member is characterized. The topology for the fuzzy unit interval is characterized among those generated by its a-closure operators.