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Jan 21, 2015 by Misrak Negatu (misrak)
MATH 6810 : General Topology
Wed, 21 Jan 2015 09:23:17 GMT
Sat, 17 Jan 2015 02:55:09 GMT
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In The Catalog Prerequisites:
MATH 6820 : Algebraic Topology
MATH 6850 : Knot Theory and Low Dimensional Topology
MATH 6860 : Topics in Knot Theory and Low Dimensional Topology
MATH 6890 : Topics in Topology
Columbian College of Arts and Sciences
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Topological spaces, bases and subbases, open sets and closed sets; continuous maps and homeomorphisms; connectedness and compactness; metric topology, product topology, and quotient topology; separation axioms; finite topological spaces, covering spaces, and fundamental groups.
The main objective of the course is to provide you with a solid topological background for your further undergraduate and/or graduate studies. In can also be considered as (one of the possible) entry points into the rigorous language of mathematics. You are expected to read and write mathematics in this course. By the end of the course, you should be able to demonstrate an understanding of fundamental topological concepts; demonstrate an understanding of main properties of topological spaces as well as interrelations between them; verify whether a given topological space possesses a specific property and make conclusions about the internal structure of this space; verify whether two topological spaces have identical topological structures and, hence, can be considered to be equivalent; further develop your writing and analytical skills and, most importantly, your critical thinking; demonstrate a capability to express your reasonings in writing and to justify them rigorously; make a distinction between correct and wrong statements about topological spaces and to support your claim in writing; provide an array of illuminating and relevant examples to illustrate and explain each major concept of the course.
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