In this article we introduce the concept of $z^circ$-filter on a topological space $X$. We study and investigate the behavior of $z^circ$-filters and compare them  with corresponding ideals, namely, $z^circ$-ideals of $C(X)$,  the ring of real-valued continuous functions on a completely regular Hausdorff space $X$. It is observed that $X$ is a compact space if and only if every $z^circ$-filter ...

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...

In this paper, we discuss the field of sampling-based motion planning. In contrast to methods that construct boundary representations of configuration space obstacles, sampling-based methods use only information from a collision detector as they search the configuration space. The simplicity of this approach, along with increases in computation power and the development of efficient collision d...

The main purpose of this paper consists of providing characterizations of the inclusion of the solution set of a given conic system posed in a real locally convex topological space into a variety of subsets of the same space de…ned by means of vector-valued functions. These Farkas-type results are used to derive characterizations of the weak solutions of vector optimization problems (including ...

General relativity can be recast as a theory of connections by performing a canonical transformation on its phase space. In this form, its (kinematical) structure is closely related to that of Yang-Mills theory and topological field theories. Over the past few years, a variety of techniques have been developed to quantize all these theories non-perturbatively. These developments are summarized ...

The topological views of a measure space provide deep insights. In this paper, the sigma-set algebraic structure is extended in Hausdorff based on locally compactable neighborhood systems without considering strictly (metrized) Borel variety. null extension gives rise to quasi sigma-semiring sigma-neighborhoods, which are rectifiable view Dieudonné n-space. concepts symmetric signed measure, un...

We define the notion of near-geodesic between points a metric space when no geodesic exists, and use this to extend Recio-Mitter’s complexity non-geodesic spaces. This has potential application topological robotics. determine explicit near-geodesics in variety cases.

A realm is a planar graph over a finite resolution grid that has been proposed as a means of overcoming problems of numerical robustness and topological correctness in spatial databases. However, in spatial databases, current data structures based on realm only deal with 2D objects, and cannot be used to describe the complex phenomena in real 3D world. In order to represent 3D spatial objects a...

Abstract Design Theory is a mathematical theory of design based on Yoshikawa’s General Design Theory and Barwise and Seligman’s Channel Theory. Classifications is the structures of Channel theory, and they are used in Abstract Design Theory in order to formulate a scheme of design. Yoshikawa discussed design in terms of topology in General Design Theory. The aim of this paper is to show propert...

the purpose of the present study is to introduce the sequence space[{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left| sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},]where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. the topological properties and inclusion relations of this space are studied. moreover, the prob...