Topology Books

A good undergraduate course in topology will prepare a student for further work in a broad variety of mathematical disciplines and will usually start by introducing the axiomatic foundations of set theory. This can be followed by a study of general topological structures and then the following topics: Cartesian products, connectedness, weak topologies, and the separation and covering axioms. In any topology course metric spaces with emphasis on convergence and compactness is crucial. After function spaces and complete spaces round out the general topics covered, there are many avenues for further development in topology.