Starplus-Compactness and Starplus-Compact Open Fuzzy Topologies on Function Spaces

Extending Lowen’s notion of strong fuzzy compactness to an arbitrary fuzzy set the notion of a starplus-compact fuzzy set is introduced. It is shown that the category of starplus-compact fuzzy topological spaces is productive, and that starplus-compactness is a good extension of the notion of compactness. It is shown that the class of starplus-compact fuzzy sets is pseudo closed hereditary and invariant under fuzzy continuous maps. Moreover, the notion of starplus-compact open fuzzy topology on a function space is introduced and its interrelations with the fuzzy topology of pointwise convergence and the fuzzy topology of joint fuzzy continuity are studied. It is shown that a fuzzy topology on a function space which is jointly fuzzy continuous on starplus-compacta is finer than the starplus-compact open fuzzy topology. Sufficient conditions on function spaces are obtained for the starplus-compact open fuzzy topology and the fuzzy topology of joint fuzzy continuity on starplus-compacta to coincide.