It is well known that the metric topology Moo66] on interval space is not compatible with the interval inclusion monotonicity property in the sense that it may exist monotonic functions which are not continuous and conversely. This paper provides a quasi-metric topology for the interval space consistent with the real line topology and whose continuous function are exactly the monotonic ones. Th...

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

Topology construction and topology maintenance are significant sub-problems of topology control. Spanning tree based algorithms for topology control are basically transmission range based type construction algorithms. The construction of an effective backbone, however, is indirectly related to the placement of nodes. Also, the dependence of network reliability on the communication path undertak...

Continuous valuations have been proposed by several authors as a way of modeling probabilistic non-determinism in programming language semantics. Let (X;O) be a topological space. A quasi-simple valuation on X is the sup of a directed family of simple valuations. We show that quasisimple valuations are exactly those valuations that extend to continuous valuations to the Alexandroff topology on ...

The early work of Mostow, Margulis and Prasad on rigidity of arithmetic lattices has evolved into a broad use of quasi-isometry techniques in group theory and low dimensional topology. The word metric on a finitely generated group makes it into a metric space which is uniquely determined up to the geometric relation called quasi-isometry, despite the fact that the metric depends on the choice o...

Many optical circuit switched data center networks (DCN) have been proposed in the last decade to attain higher capacity and topology reconfigurability, though commercial adoption of these architectures minimal. One major challenge face is difficulty handling uncertain traffic demands using switches (OCS) with high switching latency. Prior works generally focused on developing fast-switching OC...