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.