A subset M of a topological space 5 is said to have a convex metric (even though S may have no metric) if the subspace M of 5 has a convex metric. It is known [5 J that a compact continuum is locally connected if it has a convex metric. The question has been raised [5] as to whether or not a compact locally connected continuum M can be assigned a convex metric. Menger showed [5] that M is conve...

the sequential $p$-convergence in a fuzzy metric space, in the sense of george and veeramani, was introduced by d. mihet as a weaker concept than convergence. here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. in such a case $m$ is called an $s$-fuzzy metric. if $(n_m,ast)$ is a fuzzy metri...

In this paper, the poset $BX$ of formal balls is studied in fuzzy partial metric space $(X,p,*)$. We introduce the notion of layered complete fuzzy partial metric space and get that the poset $BX$ of formal balls is a dcpo if and only if $(X,p,*)$ is layered complete fuzzy partial metric space.

Network Coordination Systems (NCS) are powerful mechanisms to efficiently predict the network latency of pairwise hosts in Internet without directly network measurement between them. Each host is embedded into a distance space where the latency between nodes is calculated according to the distant function defined by the space with assigned coordination of hosts. In terms of the properties of di...

The main bottleneck of the research in metric space searching is the so-called curse of dimensionality, which makes the task of searching some metric spaces intrinsically difficult, whatever algorithm is used. A recent trend to break this bottleneck resorts to probabilistic algorithms, where it has been shown that one can find 99% of the elements at a fraction of the cost of the exact algorithm...

The main bottleneck of the research in metric space searching is the so-called curse of dimensionality, which makes the task of searching some metric spaces intrinsically diicult, whatever algorithm is used. A recent trend to break this bottleneck resorts to probabilistic algorithms , where it has been shown that one can nd 99% of the elements at a fraction of the cost of the exact algorithm. T...

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...