This is an advertisement for my book published in 1988 R.Brown, TOPOLOGY: a geometric account of general topology, homotopy types and the fundamental groupoid, Ellis Horwood/Simon and Schuster, ISBN 0-7458-0231-1 38.50 pounds(UK) 0-7458-0231-1 $62.95 (USA), 460pp I am not sure if it has been well advertised in the USA, so the existence of the Category Theory Bulletin seems a good opportunity to get the book better known. It is a revised version of the 1968 book published by McGraw Hill. There are new sections on: compactifications; the compact-open topology and the convenient category of k-spaces; fibrations of groupoids and exact sequences; the Jordan Curve Theorem ( a new proof using the groupoid material). The Chapter on Covering Spaces includes 40 pages of new material:the equivalence between coverings of spaces and coverings of groupoids; induced coverings and pullbacks; applications to subgroup theorems in group theory; orbit space and orbit groupoids; the computation of orbit groupoids: quotients and semidirect products. In particular these last sections contain material on computing the fundamental group of an orbit space under a discontinuous action of a group. An important aspect of the book is the use of universal properties, and the thorough treatment of 1-dimensional homotopy theory using the fundamental groupoid rather than fundamental group. So the book contains much of the basic algebra of groupoids, and some introductory material on categories and functors. Each Chapter ends with notes commenting on the historical background. ===========================
participants (1)
-
MAS010@vaxa.bangor.ac.uk