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Description
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This text is designed to be covered in one semester by typical math majors; however, it is still quite rigorous, modeling for the students how one writes precise proofs. It covers the essentials of point-set topology in a relatively terse presentation, with lots of examples and motivation along the way. The introductory chapter attempts to explain what topology is in the context of what math majors have usually seen in their previous coursework. Along with the standard point-set topology topics (connected spaces, compact spaces, separation axioms, and metric spaces), the author includes path-connectedness, and a chapter on constructing spaces from other spaces (including products, quotients, etc.). The text culminates in two "capstone" chapters, each independent of the other, so that the instructor may choose which subject best suits his/her views and students. The two capstone chapters are The Classification Theorem for Compact, Connected Surfaces and Fundamental Groups and Covering Spaces, with Applications. The geometric and algebraic parts of topology are introduced in the capstone chapters.
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