CONTINUOUS FLOW ON UNIFORM STRUCTURE OF FAMILY \(F(T,X)\)

Abstract

Let \(F(T,X)\) be a family of all continuous functions defined on \(T\) with values in \(X\), where \(T\) is Hausdorff topological abelian group, locally compact, \((Y,\mathcal{V})\) Hausdorff uniform space and \(X=Y^T\). The family \(F(T,X)\) we can endow with the relative uniformity of uniform convergence on compacta. The mapping \(\phi:F\times T\to F\) defined by \(\phi(f,t)=f_t\), where \(f_t(s)=f(t\oplus s)\), defines a continuous flow on structure \(F(T,X)\).