Fast complete locally convex linear topological spaces (Q1821298)

Summary: This is a study of the the relationship between the concepts of fast completeness and other well-known concepts. It is proved that every sequentially complete space is fast complete and an example of a fast complete but not sequentially complete space is presented. In case \(E\) is a metrizable space the concepts of completeness and fast completeness are the same. Some of the implications of fast completeness are: A fast complete bornological space is ultrabornological, a fast complete infrabarrelled space is barrelled and for fast complete spaces the weak\(^*\) bounded sets of \(E'\) are always strongly bounded.