The present paper introduces the notion of the complete fuzzy norm on a linear space. And, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. Some characterizations of their properties are obtained.

One approach to the development of pervasive systems is based on the notion of Personal Smart Spaces (PSSs). A PSS is implemented as an ad hoc network and may be either fixed or mobile. When one PSS encounters another, communication is established between them. This may be used to alert one user to the presence of another, or a fixed smart space to the presence of a mobile user. There is consid...

In an earlier paper, we developed general techniques which can be used to study the set of homotopy classes of maps between the classifying spaces of two given compact Lie groups. Here, we describe more precisely the general strategy for doing this; and then, as a test of these methods, apply them to determine the existence and uniqueness of (potential) maps BG −→ BG′ studied earlier by Adams a...

It is well-known that any pair of closed orientable 3-manifolds are related by a finite sequence of Dehn surgeries on knots. Furthermore Kawauchi showed that such knots can be taken to be hyperbolic. In this article, we consider the minimal length of such sequences connecting a pair of 3-manifolds, in particular, a pair of lens spaces.