I only found this book incidentally while looking at Engelking's more well-known "General Topology". I posted a link here.
https://www.scribd.com/doc/312511274/Engelking-Sieklucki-Topology-a-Geometric-Approach
Has anyone else ever heard of or read this book? Do you think it would be a good first book for an introduction to algebraic topology?
The only review of this (translation from Polish) I could find is the following:
http://michhaz.home.xs4all.nl/reviews/AAA_1272.html
The reviewer seems to consider the book as an introduction to general topology, despite the fact it seems to cover primarily topics which are prerequisites for algebraic/differential topology.
(Which is good by the way for me -- these are the subjects I want to learn.)
It seems like it might be a good simple introduction to these topics, assuming that the prerequisites really are as basic as stated; after a first chapter on metric spaces which anyone who has taken a course in real analysis could probably skip, it goes on to discuss
- Polyhedra/Simplicial Complexes
- Homotopy
- "The topology of Euclidean space" (first section about maps into spheres)
- Manifolds
- countable products of metric spaces, spaces of maps, absolute retracts, dimension
I like the idea that it might be possible to start with simplexes, since I am familiar with them from linear programming, and they are supposed to have applications to computational topology (one of the reasons I want to understand basic algebraic topology, the other being able to understand manifolds/differential geometry/differential topology).