TopologyExamTopics - Topology Qualifying Exam Topics...

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Topology Qualifying Exam Topics Covered MAT 661 Point Set Topology Topological Spaces: Topologies, neighborhoods, basis, closure operations, continuity, product and quotient topologies. Topological Properties: Separation axioms, compactness, local compactness, connectedness, local connectedness, path connectedness, separability, first and second axioms of countability. Metric Spaces: Cauchy sequences and completeness, compactness. Additional Topics: Urysohn Lemma and Metrization Theorem, Tietze Extension Theorem, topologies of pointwise and uniform convergence. Reference: 1. J. R. Munkres, Topology, Second Edition , Sections 12-35, 43, 45-46. Introductory Algebraic Topology Fundamental Group: The fundamental group and induced homomorphims, role of the base point, simple connectivity, fundamental group of the circle, applications. References: 1. J. R. Munkres, Topology, Second Edition , Sections 51-59. 2.
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This note was uploaded on 06/19/2011 for the course MATH 661 taught by Professor Na during the Spring '11 term at University of North Carolina School of the Arts.

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