Re: looking for Fréchet's 1906 Ph.D. dissertation introducing metric spaces

Dan wrote:

Does anyone know of any online archives where I can
find Maurice Fréchet's 1906 Ph.D. dissertation
"Sur quelques points du calcul fonctionnel" ? It is
supposed to be the first paper to introduce the concept
of a metric space (even though the term "metric space"
itself is due to Hausdorff).

I think that Fréchet's 1906 dissertation may have
been published in the same year in the journal
"Rendiconti del Circolo Mathematico di Palermo",
volume 22, pages 1-74. Does anyone know where I
could find this version of Fréchet's work?

I have asked basically this same question about 3 weeks
ago in another post. I hope I don't annoy anyone by
asking the same question twice.

I don't believe this journal is on-line, at least not
freely available. Most large U.S. state universities
will have it, if you're in the U.S. However, assuming
you can read French, you may find much of the motivation
and approach difficult to follow, unless you have a
good knowledge of the point set theory of the time. For
example, limit points and closed sets and the Cantor-Bendixson
theorem are central concepts, while the notion of an open
set may not even appear. Also, much of the motivation
springs from generalizing and organizing these notions
that were then beginning to be applied to collections of
curves and collections of functions, which Volterra and
others had been introducing in their study of the calculus
of variations and (what we now know as) the beginnings
of functional analysis.

The following will be very useful if you want to
study Frechet's thesis:

Angus E. Taylor, "A study of Maurice Fréchet I [II] {III}",
Archive for History of Exact Sciences 27 (1982) [34 (1985)]
{37 (1987)}, 233-295 [279-380] {25-76}.

Michael Bernkopf, "The development of function spaces with
particular reference to their origins in the integral
equation theory", Archive for History of Exact Sciences
3 (1966), 1-96.

C. E. Aull and R. Lowen (editors), "Handbook of the
History of General Topology", Kluwer Academic Punlishers,
3 volumes, 1997 & 1998 & 2001.

Dave L. Renfro

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