Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
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, T) by means of a map σ:Ix⟶I(I=[0,1]),
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 α-neighbourhoods and α−Ti
separation axioms which extend the usual ones in General Topology.
In particular, our α-Hausdorff fuzzy space agrees with α{*}
-Rodabaugh Hausdorff fuzzy space when (X, T) is interpreservative
or α-locally minimal