We present an alternative derivation and geometrical formulation of Verlinde topological field theory, which may describe scattering at center of mass energies comparable or larger than the Planck energy. A consistent truncation of 3+1 dimensional Einstein action is performed using the standard geometrical objects, like tetrads and spin connections. The resulting topological invariant is given ...

Exciton scattering theory attributes excited electronic states to standing waves in quasi-one-dimensional molecular materials by assuming a quasi-particle picture of optical excitations. The quasi-particle properties at branching centers are described by the corresponding scattering matrices. Here, we identify the topological invariant of a scattering center, referred to as its winding number, ...

in this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. we also investigate effect to fuzzy soft connectedness. moreover, c_i-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.

In this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. It gives some criterions to study locally convex topological spaces in a discrete approach.

In this paper, we study the separtion axioms $T_0,T_1,T_2$ and $T_{5/2}$ on topological and semitopological residuated lattices and we show that they are equivalent on topological residuated lattices. Then we prove that for every infinite cardinal number $alpha$, there exists at least one nontrivial Hausdorff topological residuated lattice of cardinality $alpha$. In the follows, we obtain some ...

Nowadays, geospatial information systems (GIS) are widely used to solve different spatial problems based on various types of fundamental data: spatial, temporal, attribute and topological relations. Topological relations are the most important part of GIS which distinguish it from the other kinds of information technologies. One of the important mechanisms for representing topological relations...

This paper describes the definition and testing of a new type of median filter for images. The topological median filter implements some existing ideas and some new ideas on fuzzy connectedness to improve, over a conventional median filter, the extraction of edges in noise. The concept of alpha-connectivity is defined and used to create an algorithm for computing the degree of connectedness of ...

In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.