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Columbian College of Arts and Sciences

Mathematics (MATH)

MATH

6810

General Topology

General Topology

Fall 2015

3

Course Type

Lecture

Default Grading Method

Letter Grade

No

No

Corequisites

20

Frequency of Offering

Term(s) Offered

Are there Course Equivalents?

No

No

Fee Type

No

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.

Uploaded a Course Syllabus

Course Attribute

Key: 5649