In this paper, we introduce the concept of ordinary smooth topology on a set X by considering the gradation of openness of ordinary subsets of X . And we obtain the result [Corollary 2.13] : An ordinary smooth topology is fully determined its decomposition in classical topologies. Also we introduce the notion of ordinary smooth [resp. strong and weak] continuity and study some its properties. A...

In higher dimensional theories, such as brane world models with quasilocalized non-Abelian gauge fields, the vacuum structure turns out to be trivial. Since the gauge theory behaves at large distances as a 4 + delta dimensional, thus the topology of the infinity is that of S(3+delta) rather than S(3). This topology does not support finite action instantonic configurations and thus the CP violat...

Topological self-stabilization is the ability of a distributed system to have its nodes themselves establish a meaningful overlay network. Independent from the initial network topology, it converges to the desired topology via forwarding, inserting, and deleting links to neighboring nodes. We adapt a linearization algorithm, originally designed for a shared memory model, to asynchronous message...

In this paper we study the conformal structure and the asymptotic behavior of properly embedded minimal surfaces of finite topology in . One consequence of our study is that when such a surface has at least two ends, then it has finite conformal type, i.e., it is conformally diffeomorphic to a compact Riemann surface punctured in a finite number of points. Except for the helicoid and a recently...

The paper investigates the variation of the spectrum of operators in infinite dimensional Banach spaces. Consider the space of bounded operators on a separable Banach space when equipped with the strong operator topology, and the Polish space of compact subsets of the closed unit disc of the complex plane when equipped with the Hausdorff topology. Then, it is shown that the unit spectrum functi...

among structured peer-to-peer systems, chord has a general popularity due to its salient features like simplicity, high scalability, small path length with respect to network size, and flexibility on node join and departure. however, chord doesn’t take into account the topology of underlying physical network when a new node is being added to the system, thus resulting in high routing latency an...

following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...

in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.