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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 1235, 43, 4546.
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 5159.
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.
 Spring '11
 NA
 Logic, Topology, Continuity

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