In [3], we started the investigation of compactness in fuzzy function spaces in FCS, the category of fuzzy convergence spaces as defined by Lowen/Lowen/Wuyts [8]. This paper goes somewhat deeper in the investigation of fuzzy function spaces using the notion of splitting and conjoining structures on fuzzy subsets. We discuss the connection to the exponential law and give several examples of such...

A notion of Hochschild cohomology HH∗(A) of an abelian category A was defined by Lowen and Van den Bergh (2005) and they showed the existence of a characteristic morphism χ from the Hochschild cohomology of A into the graded centre Z∗(Db(A)) of the bounded derived category of A. An element c ∈ HH2(A) corresponds to a first order deformation Ac of A (Lowen and Van den Bergh, 2006). The problem o...

In this paper we introduce the concept of mixed fuzzy ideal topological spaces in Lowen sense. AMS subject classification: 54A40.

Intra-host dynamics of influenza virus reassortment 1 Hui Tao, John Steel and Anice C. Lowen* 2 3 Department of Microbiology and Immunology, Emory University School of Medicine, 4 Atlanta, Georgia 30322. 5 6 Running title: Dynamics of influenza virus reassortment 7 Abstract word count: 246 8 Importance word count: 145 9 10 *Address Correspondence: 11 Anice C. Lowen 12 Department of Microbiology...

The original definition of a topological space given by Hausdorff used neighborhood systems. Lattice-valued maps appear in this context when you identify a topology with a monoid in the Kleisli category of the filter monad on SET. H?hle’s notion of a lattice-valued topology [2] uses the same idea and it’s inspired in the classical lattice-valued topologies. Ltopological spaces are motivated by ...

Using the idea of approach space due to Robert Lowen [Approach spaces. The missing link in the topology-uniformitymetric triad], we define the notion of fuzzy approach spaces as a natural generalization of fuzzy metric spaces due to Kramosil and Michalek [Kybernetika , 11, 1975, 336–344] and prove some properties of fuzzy approach spaces. Keywords— Approach spaces, Fuzzy approach spaces, Fuzzy ...

Since Chang [2] introduced fuzzy theory into topology, many authors have discussed various aspects of fuzzy topology. It is well known that weakly induced and induced topological spaces play an important role in L-topological spaces (see book [8]). According to their value ranges, L-topological spaces form different categories. Clearly, the investigation on their relationships is certainly impo...

This paper presents an approach to the fuzzification of complete lattices. This kind of fuzzification is a functor from the category of complete lattices to the category of completeL-ordered sets. It not only can be considered as an algebraic representation of the Lowen functor ωL, but also can characterize the stratification of L-topological spaces and the underlying set of Hutton unit interval.