Subject: categories: Now available: Topology and groupoids, by Ronald Brown

From: "Ronald Brown" <[email-masked]>
Date: Fri, 3 Mar 2006 22:02:29 -0000

This is a retitled, revised, refined, expanded edition of my topology book
previously published in 1968 and 1988, and now available at the amazing
price of $23.99.
To order, please use the following link:

http://www.booksurge.com/product.php3?bookID=GPUB05314-00001&affiliateID=A001356

Their Global Publishing System should allow more local printing and
delivery.

538 pages. List of chapters:
Some topology on the real line
Topological spaces
Connected spaces, compact spaces
Identification spaces and cell complexes
Projective and other spaces
The fundamental groupoid
Some combinatorial groupoid theory
Cofibrations
Computation of the fundamental groupoid
Covering spaces, covering groupoids
Orbit spaces, orbit groupoids
Conclusion

It combines a geometric and a categorical approach, where the latter allows
clear analogies between areas of mathematics, such as topology and algebra.
This is seen very clearly in the chapters on covering spaces and orbit
spaces.

Here are some examples of topics covered not available in other texts at
this level:
the initial topology on joins of spaces;
the convenient category of k-spaces in the non Hausdorff case;
a gluing theorem for homotopy equivalences;
the Phragmen-Brouwer property, proved using the groupoid van Kampen theorem,
and applied to the Jordan Curve theorem;
the equivalence between covering maps of spaces and covering morphisms of
groupoids;
the fundamental groupoid of an orbit space by a discontinuous action of a
group as the orbit groupoid of the fundamental groupoid.

The book is graced by a cover by John Robinson and Ben Dickens.

Ronnie Brown
www.bangor.ac.uk/r.brown
www.popmath.org.uk