The aim of this paper is to present a fuzzy counterpart method of constructing the Hausdorff quasi-uniformity of a crisp quasi-uniformity. This process, based on previous works due to Morsi cite{Morsi94} and Georgescu cite{Georgescu08}, allows to extend probabilistic and Hutton $[0,1]$-quasi-uniformities on a set $X$ to its power set.  In this way, we obtain an endofunctor for each one of the c...

We use the notion of uniform measure equivalence to prove that the Novikov-Shubin invariants resp. the capacities of amenable groups are invariant under quasi-isometry. Further, we comment on the connection to Gaboriau’s theorem on the invariance of L-Betti numbers under orbit equivalence.

In cite{Kats84}, Katsaras introduced a method for constructing a Hu-tton $[0,1]$-quasi-uniformity from a crisp uniformity. In this paper we present other different methods for making this based mainly in the concept of a fuzzy uniform structure. Furthermore, we prove that some of these methods preserve the completeness property of the quasi-uniformity.  Moreover, we also show that Katsaras' con...

We lay down the foundations for a pointfree theory of Pervin spaces. A space is set equipped with bounded sublattice its powerset, and it known that these objects characterize those quasi-uniform spaces are transitive totally bounded. The notion space, which we call Frith frame, consists frame generating sublattice. In this paper introduce study category frames show classical dual adjunction be...

In this paper, L-convex ?*-remotehood system is introduced and some characterizations of both L-convexity remotehood are obtained. Further, ?*-remote mapping presented its properties investigated. Based on this, quasi-uniformity quasiuniformity preserving introduced. It proved that quasi-uniform space Lconvex mutually induced. addition, the category spaces can be embedded into spaces.