The equicontinuous structure relation and extension of continuous equivariant functions (Q1820461)

Let \(f: A\to B\) be a morphism of a category \({\mathcal K}\), then an object C of \({\mathcal K}\) is called an injective object of f if for every morphism \(g: A\to C\) there exists a morphism \(h: B\to C\) with \(g=h\cdot f\). Let G be a topological group. Every equicontinuous G-space (K,\(\alpha)\) where K is a metrizable compact convex subset of a locally convex topological vector space is an injective object of a closed equivariant embedding \(i:(A,\pi)\to (X,\pi)\) in the category of compact Hausdorff G-spaces if and only if every almost periodic function on A can be extended to an almost periodic function on X. This fact is proved using methods of topological dynamics.