### MAT 530 (Fall 1995) Topology/Geometry I

## Text and References

**Text**

John G. Hocking and Gail S. Young, *Topology*,
Dover Publications, Inc., New York 1988. (This work was first
published, by Addison-Wesley, in 1961)

This is an excellent book that gives the motivation for
topological concepts along with rigorous definitions, and
does a good job of communicating why topologists love
topology. Some of the terminology is somewhat archaic.
The concept of category appears only implicitly in the
first section. The authors use *transformation* where
today one more commonly hears *map* or *mapping*, and
*separated* for our *disconnected* (beware a
possible confusion with the French usage of *séparé*
to mean *Hausdorff* !).

**References**

Nicolas Bourbaki, *General Topology*

John Kelly, *General Topology*, Van Nostrand, Princeton NJ 1955.

Includes all you ever wanted to know about the Axiom
of Choice and more. This book is a model of elegant exposition; you
know you're in the hands of a master.

James Munkres, *Topology, a First Course*, Prentice Hall, Englewood
Cliffs NJ 1975

Leopoldo Nachbin, *The Haar Integral*, Van Nostrand, Princeton NJ 1965.

Useful to us for the transparent proof of the Tychonoff
Theorem.

André Weil, Sur les théorèmes de de Rham,
*Commun. Math. Helv.* (1952)
119-145

This paper, which gives proofs of de Rham's theorems
relating the
de Rham, singular and Cech homology and cohomology for smooth manifolds,
is constructed like a beautiful watch. There is not a superfluous comma,
and never an inelegant turn of phrase. A low-key conversation with a
mathematical giant. (The proofs, organized by double complexes, are
the modern sheaf-theoretic proofs *avant la lettre*. Everything
is there but the terminology, and everything is completely explicit.)

Hassler Whitney, *Annals of Math.* **37** (1936) 668-672

Thanks to Larry Cruvant for this reference.

Hassler Whitney, Geometric Integration Theory, Princeton Univ. Press,
Pronceton New Jersey 1957.