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Further Reading > General Topology
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General Topology One of the purest and most intellectually challenging branches of modern mathematics, this is not a subject for the faint hearted. You'll need to read these books carefully, and a detailed understanding may emerge only slowly, but when it does emerge it'll have been worth every minute. Taking your mind for a stroll around an abstract topological space, where even basic ooncepts like distance and dimension may not mean very much, is a joy few humans have ever experienced. S. Willard General Topology One of the best reference guides to the subject ever written, Willard's book covers everything the aspiring topologist needs to know, and certainly supplies more than enough information for a potential PhD student to choose their initial area of specialisation. The chapters are split intelligently into sub-topics which move at a sensible pace from its introductory notes on essential set theory, through subspaces, products, compactness, separation and countability axioms, compactifications, and function spaces. Many of the "standard spaces" of general topology are introduced and examined in the large number of related problems accompanying each section. And for those wanting a bit more context than a maths book normally provides there's a detailed collection of historical notes for each chapter.