Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4343

 Title: Fuzziness in Chang's fuzzy topological spaces Authors: Gregori, ValentínVidal, Anna Keywords: fuzzy topologygradation of opennessfuzzy point Issue Date: 1999 Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche Citation: Valentín Gregori and Anna Vidal, "Fuzziness in Chang's fuzzy topological spaces", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 30 (1999) suppl., pp. 111-121. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics30 (1999) suppl. Abstract: It is known that fuzziness within the concept of openness of a fuzzy set in a Chang's fuzzy topological space (fts) is absent. In this paper we introduce a gradation of openness for the open sets of a Chang jts (X, $\mathcal{T}$) by means of a map $\sigma\;:\; I^{x}\longrightarrow I\left(I=\left[0,1\right]\right)$, which is at the same time a fuzzy topology on X in Shostak 's sense. Then, we will be able to avoid the fuzzy point concept, and to introduce an adeguate theory for $\alpha$-neighbourhoods and $\alpha-T_{i}$ separation axioms which extend the usual ones in General Topology. In particular, our $\alpha$-Hausdorff fuzzy space agrees with $\alpha${*} -Rodabaugh Hausdorff fuzzy space when (X, $\mathcal{T}$) is interpreservative or $\alpha$-locally minimal. URI: http://hdl.handle.net/10077/4343 ISSN: 0049-4704 MS Classification: 54A40 Appears in Collections: Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.30 (1999) s.

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