Abstract:For a system $V$ of weights on a completely regular Hausdorff space $X$ and a Hausdorff topological vector space $E$, let $ CV_b(X,E)$ and $ CV_0(X,E)$ respectively denote the weighted spaces of continuouse $E$-valued functions $f$ on $X$ for which $ (vf)(X)$ is bounded in $E$ and $vf$ vanishes at infinity on $X$ all $ v\in V$. On $CV_b(X,E)(CV_0(X,E))$, consider the weighted topology, which is Hausdorff, linear and has a base of neighbourhoods of 0 consising of all sets of the form: $ N(v,G)=\{f:(vf)(X)\subse… Show more
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