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Fuzziness in Chang's fuzzy topological spaces
Gregori, Valentín
Vidal, Anna
1999
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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
30 (1999) suppl.
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
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.
Languages
en
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