The evolution of small irregularities in a topological defect which propagates on a curved background spacetime is examined. These are described by a system of coupled scalar wave equations on the worldsheet of the unperturbed defect which is not only manifestly covariant under world sheet diffeomorphisms but also under local normal frame rotations. The scalars couple both through the surface t...

The Tangle toy [Zaw15, Zaw85] is a topological manipulation toy that can be twisted and turned in a variety of different ways, producing different geometric configurations. Some of these configurations lie in 3D space while others may be flattened into planar shapes. The toy consists of several curved, quarter-circle pieces fit together at rotational/twist joints. Each quarter-circle piece can ...

The fractionally charged quasiparticles appearing in the 5/2 fractional quantum Hall plateau are predicted to have an extra nonlocal degree of freedom, known as topological charge. We show how this topological charge can block the tunneling of these particles, and how such topological blockade can be used to read out their topological charge. We argue that the short time scale required for this...

We compute instanton corrections to correlators in the genus-zero topological subsector of a (0, 2) supersymmetric gauged linear sigma model with target space P × P, whose left-moving fermions couple to a deformation of the tangent bundle. We then deduce the theory’s chiral ring from these correlators, which reduces in the limit of zero deformation to the (2, 2) ring. Finally, we compare our re...

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

in this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the hypercyclicity criterion. we characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional banach space .

‎for a given measure space $(x,{mathscr b},mu)$ we construct all measure spaces $(y,{mathscr c},lambda)$ in which $(x,{mathscr b},mu)$ is embeddable‎. ‎the construction is modeled on the ultrafilter construction of the stone--v{c}ech compactification of a completely regular topological space‎. ‎under certain conditions the construction simplifies‎. ‎examples are given when this simplification o...

In this article, we present the concept of supra paracompact spaces and study its basic properties. We elucidate its relationship with supra compact spaces and prove that the property of being a supra paracompact space is weakly hereditary and topological properties. Also, we provide some examples to show some results concerning paracompactness on topology are invalid on supra topology. Finally...

An object $X$ of a category $mathbf{C}$ with finite limits is called exponentiable if the functor $-times X:mathbf{C}rightarrow mathbf{C}$ has a right adjoint. There are many characterizations of the exponentiable  spaces in the category $mathbf{Top}$ of topological spaces. Here, we study the exponentiable objects in the category $mathbf{STop}$ of soft topological spaces which is a generalizati...