= Strong dual topology
{title2=$\beta(E',E)$}
For a <locally convex space> $E$, the <strong dual topology> on its <continuous dual space> $E'$ is generated by seminorms $p_B(T)=\sup_{\varphi\in B}|\langle T,\varphi\rangle|$, where $B$ runs through the <bounded sets in a topological vector space> $E$. Convergence therefore means uniform convergence of pairings on every such set. For the <Schwartz space>, the defining boundedness is boundedness of every Schwartz seminorm, rather than one norm or one common compact support.
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