Sequential Compactness of X Implies a Completeness Property for C(X)
Sequential Compactness of X Implies a Completeness Property for C(X)
A locally convex Hausdorff topological vector space is said to be quasicomplete if closed bounded subsets of the space are complete, and von Neumann complete if closed totally bounded subsets are complete (equivalently, compact). Clearly quasi-completeness implies von Neumann completeness, and the converse holds in, for example, metrizable locally convex …