Most chapters are followed by exercises adding details to the theory (in
some cases doing duty for proofs omitted in the text), starred exercises whose
results will be used later in the text, occasional unsolved problems, and a
major unsolved problem. The major unsolved problems are Problems A, Bi,
B2, B3 C, D. Not all are precisely posed, but all describe areas in which
there seems to be good reason to expect interesting results although the
results now known are quite unsatisfactory. The appendix might reasonably
be counted as another such problem, for it gives several characterizations
of the line and draws attention to the plane.
A preliminary version of this book was prepared as a set of lecture notes at
Purdue University in 1960. The wofk of writing it has been supported at
Purdue by the Office of Naval Research and at the University of Washing-
ton by the National Science Foundation. I am indebted to Professors M.
Henriksen and M. Jerison for helpful criticisms of the Purdue lecture notes.
Professors E. Alfsen, H. Corson, J. de Groot, E. Hewitt, E. Michael, D.
Scott, and J. Segal have contributed some criticisms and suggestions during
the writing of the final version. Many blemishes surviving that far were
caught and exposed by Professor P. E. Conner for the Editorial Committee.
But none of my distinguished colleagues has assumed responsibility for the
remaining errors, which are mine.