Kasriel R. Undergraduate Topology 2009

Textbook in PDF format

General topology offers a valuable tool to students of mathematics, particularly in courses involving complex, real, and functional analysis. This introductory treatment is essentially self-contained, and it features explanations and proofs that relate to every practical aspect of point-set topology. It will prove valuable to undergraduate mathematics majors as well as to graduate students and professionals pursuing mathematics research.
Author Robert H. Kasriel, who taught at Georgia Tech for many years, begins with reviews of elementary set theory and Euclidean n-space. The following chapters offer detailed studies of metric spaces and applications to analysis. A survey of general topological spaces and mappings includes considerations of compactness, connectedness, quotient spaces, net and filter convergence, and product spaces. Nearly every one of the 112 sections in this book concludes with a set of exercises that reinforce materials already covered and prepare students for subsequent chapters