Topological vector spaces
The first five sections deliver the general setting of the theory (topological vector spaces, metrizability, projective and inductive limits, topological direct sums). In sections 6-10 we investigate the class of "barrelled" topological vector spaces which is important also in this general theory. The main part of these sections is take by theorems on linear mappings (the Banach-Steinhaus theorem, closed graph theorems, open mapping theorems). Section 11 introduces the "bornological" spaces, and in section 12 we deal with spaces of linear mappings and their topologies. Interesting generalizations of the class of (DF)-spaces are given in sections 15-17 by considering the following property: a subset, which is "large enough", is a neighborhood of 0, if and only if it includes a neighborhood on all bounded balanced sets. Finally, section 18 interprets and completes the foregoing considerations for (DF)-spaces
eBook, English, 1978
Springer-Verlag, Berlin, 1978