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.

In this paper, we introduce and study a new topology related to a self mapping on a nonempty set.Let X be a nonempty set and let f be a self mapping on X. Then the set of all invariant subsets ofX related to f, i.e. f := fA X : f(A) Ag P(X) is a topology on X. Among other things,we nd the smallest open sets contains a point x 2 X. Moreover, we find the relations between fand To f . For insta...

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuz...

The purpose of the present work is to introduce the concept of bifuzzy core of a fuzzy automaton, which induces a bifuzzy topology on the state-set of this fuzzy automaton. This is shown that this bifuzzy topology can be used to characterize the concepts such as bifuzzy family of submachines, bifuzzy separable family and bifuzzy retrievable family of a fuzzy automaton.