Preface
Analysis and its Adhesions
Between 1946 and 1990 I had thousands of students; in the very economical
French system with its auditoria for two hundred people or more, this was
not difficult. On several occasions I felt the desire to write a book which,
presupposing only a minimal level of knowledge and a taste for mathematics,
would lead the reader to a point from which he (or she) could launch himself
without difficulty into the more abstract or more complicated theories of the
XX th century. After various attempts I began to write it for Springer-Verlag
in the Spring of 1996.
A long-established house, with unrivalled experience in scientific publishing in general and mathematics in particular, Springer seemed to be by far
the best possible publisher. My dealings with their mathematical department
over six years have quite confirmed this. As, furthermore, Catriona Byrne,
who has responsibility for author relations in this sector, has been a friend
of mine for a long time, I had no misgivings at confiding my francophone
production to a foreign publisher who, though not from our parish, knows its
profession superlatively.
My text has been prepared in French on computer, in DOS, with the
aid of Nota Bene, a perfectly organized, simple and rational American word
processor; but it is hardly more adapted to mathematics than the traditional
typewriters of yesteryear: greek letters, E, J, E have to be written by hand
on the printout, something I had been doing anyway since my first 1946
typewriter. I eventually devised a coding system, for instance [[alpha]] for
greek letters, that made it easier to translate the NB files into TEX by using
global commands. But apart from simple formulae in the main text, most of
the others had to be typeset again for the French version.
The excellent English translation has been much easier to do since
Dr Spain, who types in TEX, had the TEX version of the French edition.
I have taken this opportunity to make some small changes to the French version.
* * *
This is not a standard textbook geared to those many students who have to
learn mathematics for other purposes, although it may help them; it is the
reader interested in mathematics for its own sake of whom I have thought
while writing. To many of the French students and particularly to many of
Analysis and its Adhesions
Between 1946 and 1990 I had thousands of students; in the very economical
French system with its auditoria for two hundred people or more, this was
not difficult. On several occasions I felt the desire to write a book which,
presupposing only a minimal level of knowledge and a taste for mathematics,
would lead the reader to a point from which he (or she) could launch himself
without difficulty into the more abstract or more complicated theories of the
XX th century. After various attempts I began to write it for Springer-Verlag
in the Spring of 1996.
A long-established house, with unrivalled experience in scientific publishing in general and mathematics in particular, Springer seemed to be by far
the best possible publisher. My dealings with their mathematical department
over six years have quite confirmed this. As, furthermore, Catriona Byrne,
who has responsibility for author relations in this sector, has been a friend
of mine for a long time, I had no misgivings at confiding my francophone
production to a foreign publisher who, though not from our parish, knows its
profession superlatively.
My text has been prepared in French on computer, in DOS, with the
aid of Nota Bene, a perfectly organized, simple and rational American word
processor; but it is hardly more adapted to mathematics than the traditional
typewriters of yesteryear: greek letters, E, J, E have to be written by hand
on the printout, something I had been doing anyway since my first 1946
typewriter. I eventually devised a coding system, for instance [[alpha]] for
greek letters, that made it easier to translate the NB files into TEX by using
global commands. But apart from simple formulae in the main text, most of
the others had to be typeset again for the French version.
The excellent English translation has been much easier to do since
Dr Spain, who types in TEX, had the TEX version of the French edition.
I have taken this opportunity to make some small changes to the French version.
* * *
This is not a standard textbook geared to those many students who have to
learn mathematics for other purposes, although it may help them; it is the
reader interested in mathematics for its own sake of whom I have thought
while writing. To many of the French students and particularly to many of