We have the following. Fix $X, (Y,d)$ polish spaces where $d$ is some bounded metricon $Y$. Assign the topology to . Topologise $Z=C^{0}(X,Y)$ induced C^{0}(X,Y)$by the metric$d(f,g)=sup_{x\in X}d(f(x),g(x))$. One Then one can tweak Kechris' proof to show, that the subspace$S$of uniformly continuous maps with bounded images, is Polish. Is it possible to show that$C^{0}(X,Y)$can be generated by$S$, using point-wise limits of$\omega$-sequences of functions? This would be a useful result. 1 We have the following. Fix$X, (Y,d)$polish spaces where$d$is some bounded metric on$Y$. Assign the topology to$Z=C^{0}(X,Y)$induced by the metric$d(f,g)=sup_{x\in X}d(f(x),g(x))\$.