This book contains a compressed introduction to the study of normed linear spaces and to that part of the theory of linear topological spaces
without which the main discussion could not well proceed.
Definitions of many terms which are required in passing can be
found in the alphabetical index. Symbols which are used throughout
all, or a significant part, of this book are indexed on page 132*. Each
reference to the bibliography is made by means of the author's name,
supplemented when necessary by a number in square brackets. The
bibliography does not completely cover the available literature, even
the most recent; each рдрег in it is the subject of a specific reference
at some point in the texf. \
The writer takes this opportunity to express thanks to the University
of Illinois, the National Science Foundation, and the University of
Washington, each of which has contributed in some degree to the
cultural, financial, or physical support of the writer, and to Mr. R. R.
Phelps, who eradicated many of the errors with which the manuscript
was infested.