## A Guide to TopologyA Guide to Topology is an introduction to basic topology for graduate or advanced undergraduate students. It covers point-set topology, Moore-Smith convergence and function spaces. It treats continuity, compactness, the separation axioms, connectedness, completeness, the relative topology, the quotient topology, the product topology, and all the other fundamental ideas of the subject. The book is filled with examples and illustrations. Students studying for exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too. |

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accumulation point basis boundary calculus called Cantor set Cauchy certainly closed sets closure collection compact set compact-open topology compactification complement connected contains continuous function critical point define dense dimension disc disjoint open sets distinct points elements embedding empty set equicontinuous equivalent Euclidean space Example family of functions Figure finite subcovering Hausdorff space height function hence Hilbert cube homeomorphism idea infinite integers interior inverse image Krantz Lebesgue number lemma level sets Mathematical metric space Morse theory noncut point open ball open cover open interval open sets paracompact partition of unity plane point x e pointwise convergence polynomial Proof Proposition pseudometric quotient topology rational numbers real line real numbers Ross Honsberger second countable Section separation axiom sequence space A space subbasis Suppose topological space topology of pointwise torus Tychanoff uniform convergence uniform space unit interval usual topology vector space Weierstrass Approximation Theorem