LINEAR SPACES A TOPOLOGY

A good introductory text on this subject should include a presentation
of its axiomatics (i.e., of the general theory of topological vector spaces), it
should treat at least a few topics in some depth, and it should contain some
interesting applications to other branches of mathematics. I hope that the
present book meets these criteria.The subject is huge and is growing rapidly. (The bibliography in
volume I of [4] contains 96 pages and goes only to 1 957.) In order to write
a book of moderate size, it was therefore necessary to select certain areas
and to ignore others. I fully realize that almost any expert who looks at the
table of contents will find that some of his or her (and my) favorite topics
are missing, but this seems unavoidable. It was not my intention to write an
encyclopedic treatise. I wanted to write a book that would open the way to
further exploration.The subject is huge and is growing rapidly. (The bibliography in
volume I of [4] contains 96 pages and goes only to 1 957.) In order to write
a book of moderate size, it was therefore necessary to select certain areas
and to ignore others. I fully realize that almost any expert who looks at the
table of contents will find that some of his or her (and my) favorite topics
are missing, but this seems unavoidable. It was not my intention to write an
encyclopedic treatise. I wanted to write a book that would open the way to
further exploration.