Near Stein-Weiss Finite Vector Field Groups in Characteristic Nearness Approximation Spaces in the Polar Complex Plane, vi

Abstract

This paper introduces results for characteristically near Stein-Weiss groups inherent in vector fields in the complex plane $\mathbb{C}$. Near groups are discerned in the context of characteristic nearness approximation spaces (cNASs). A characteristic of a Stein-Weiss group is a holomorphic mapping $\varphi:\Omega\in 2^{\mathbb{C}}\to\mathbb{C}$ defined by $\varphi(t)=e^{jt}$, which defines a vector field in the complex plane. All characteristic vectors emanate from the same fixed point in $\mathbb{C}$, namely, 0.