In this paper we introduce a new notion of generalized metric, called i-metric. This generalization is made by changing the valuation space of the distance function. The result is an interesting distance function for the set of fuzzy numbers of Interval Type with non negative fuzzy numbers as values. This example of i-metric generates a topology in a very natural way, based on open balls. We pr...

This article introduces interior and closure operators with inclusion degree considered within a crisp or fuzzy topological framework. First, inclusion degree is introduced in an extension of the interior and closure operators in crisp topology. This idea is then introduced in fuzzy topology by incorporating a relaxed version of fuzzy subsethood. The introduction of inclusion degree leads to a ...

0 Introduction For n 2, Let M n be a nite convex, not necessarily smooth, hypersur-face in Euclidean space R n+1 containing the origin. More precisely, M n is the boundary of some convex domain in R n+1 containing a neighborhood of the origin. We write M n = fR(x) = (x)x j x 2 S n g, where is a function from S n to R +. Let : M n ! S n denote the generalized Gauss map, namely, (Y) is the set of...

The main result can be stated roughly as follows: Let M be an Alexandrov space, Ω ⊂M an open domain and f : Ω→ R a harmonic function. Then f is Lipschitz on any compact subset of Ω. Using this result I extend proofs of some classical theorems in Riemannian geometry to Alexandrov spaces.

Motivated by research on how topology may be a helpful foundation for building information modeling (BIM), a relational database version of the notions of chain complex and chain complex morphism is defined and used for storing cw-complexes and their morphisms, hence instances of building projects and different views upon them, into relational databases. In many cases, this can be done without ...

The concept of fuzzy super irresolute function was considered and studied by Šostak's (1985). A comparison between this type and other existing ones is established. Several characterizations, properties, and their effect on some fuzzy topo-logical spaces are studied. Also, a new class of fuzzy topological spaces under the terminology fuzzy S *-closed spaces is introduced and investigated. 1. In...

A generalized fuzzy topological space called countable fuzzy topological space has already been introduced by the authors. The generalization has been performed by relaxing the criterion of preservation of arbitrary supremum of fuzzy topology to countable supremum. In this paper the notion of fuzzy compactness called c-compactness has been initiated and various properties are studied. Other rel...

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...

The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...