Metric Linear Spaces

[From the Preface]

The definition of linear metric spaces was given by Frechet (1926). The basic facts in the theory of linear metric spaces were proved before 1940 (largely by Banach and his collaborators).

At the beginning the investigations concentrated mainly on the theory of normed spaces, and the appearance of the theory of distribution induced fast progress of investigations in the theory of locally convex spaces.

The development of the theory of integral operators and the theory of stochastic processes has aroused interest in the theory of non-locally convex spaces. Several papers dealing with this topic have been published, but this book has been the first monograph devoted to the subject.

The first edition of this book was published ten years ago in Monografie Matematyczne, due to the encouragement of Professors K. Borsuk and K. Kuratowski. Since then the theory of non-locally convex spaces has been intensively developed. New applications of the theory have been discovered in probability theory, in the theory of integral operators and in analytic functions. Several of the open problems described in the first edition have been solved.

For these reasons the second edition is a rewritten and enlarged version of the original book.