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...

In this paper, we define and study the Perov fuzzy metric space topology induced by space. We prove Banach contraction theorems. Moreover, devised new results for Kramosil Michálek spaces. process, some about multidimensional common fixed points as coupled/tripled point are derived from our main results.

One of the important characteristics topological phases matter is topology underlying manifold on which they are defined. In this paper, we present sensitivity such to topology, by studying phase transitions induced due change in boundary conditions. We claim that these accompanied broken symmetries excitation space and gain further insight analyze various signatures like ground state degenerac...

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. ...