Preface: Four ways to use this book
Introduction: The enchanting world of topology
Cardinality : to infinity and beyond
Topological spaces : fundamentals
Bases, subspaces, products : creating new spaces
Separation properties : separating this from that
Countable features of spaces : size restrictions
Compactness : the next best thing to being finite
Continuity : when nearby points stay together
Connectedness : when things don't fall into pieces
Metric spaces : getting some distance
Transition from point-set topology to algebraic and geometric topology : similar strategies, different domains
Classification of 2-manifolds : organizing surfaces
Fundamental group : capturing holes
Covering spaces : layering it on
Manifolds, simplexes, complexes, and triangulability : building blocks
Simplicial Z₂-homology : physical algebra
Applications of Z₂-homology : a topological superhero
Simplicial Z-homology : getting oriented
Singular homology : abstracting objects to maps
The end : a beginning-reflections on topology and learning.
