A note on the completeness of the space of bounded sequences with values in a Hausdorff locally convex topological vector space (Q5929771)

Let \(X\) be a Hausdorff locally convex topological linear space and let \(lf(X)\) be the space of bounded X-valued sequences. In this note, the author proves that the space \(lf(X)\) is complete if and only if the space \(X\) is complete, and this is also equivalent to the completeness of the subclass of statistical convergent sequences in the space \(lf(X)\).