Topology on $\mathfrak {G}$

Abstract

This chapter introduces a compact Hausdorff topology $\tau$ on $\mathfrak G$ and from theory already developed derives the existence of an isometric isomorphism between the Banach algebra $\text {L}_{\infty }$ and the space of real-valued continuous functions C($\mathfrak G$, $\tau$). This leads to, among other things, a duality between weak convergence in $\text {L}_{\infty }$ and weak convergence in C($\mathfrak G$, $\tau$).