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. ᮊ
We study several uniformities on a function space and show that the fuzzy topology associated with the fuzzy uniformity of uniform convergence is jointly fuzzy continuous on C f (X, Y) , the collection of all fuzzy continuous functions from a fuzzy topologi-cal space X into a fuzzy uniform space Y. We define fuzzy uniformity of uniform convergence on starplus-compacta and show that its corresponding fuzzy topology is the starplus-compact open fuzzy topology. Moreover, we introduce the notion of fuzzy equicontinuity and fuzzy uniform equicontinuity on fuzzy subsets of a function space and study their properties. 2000 AMS Classification: 03E72, 04A72, 54A40, 54C35, 54D30, 54E15. Keywords: Starplus-compact open fuzzy topology, fuzzy uniformity of uniform convergence, jointly fuzzy continuous fuzzy topology, fuzzy uniformity of uniform convergence on starplus-compacta, fuzzy equicontinuity, fuzzy uniform equicontinuity.
We introduce and investigate the notion of strongly δ-I-continuous functions, R-I-continuous functions and strongly R-I-continuous functions in ideal topological spaces.We obtain some characterizations and properties of these functions. We also study the relationship between these functions and some other weak and strong forms of continuities in ideal topological spaces.
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