Math 121: General Course Outline
Catalog Description
    121. Introduction to Topology. (4) Requisite: course 131A. Metric and topological spaces, completeness, compactness, connectedness, functions, continuity, homeomorphisms, topological properties.
Textbook
    T. Gamelin and R. Greene, Introduction to Topology, 2nd Ed., Dover.
Reviews & Exams
    The following sample schedule, with textbook sections and topics, is based on 25 lectures. Assigned homework problems play an important role in the course, and there is usually a midterm exam.
Schedule of Lectures

Lecture
Section
Topics
1-3
1.1-4
Metric spaces, open and closed sets; completeness, Baire category theorem; euclidean space
4-5
1.5
Compactness, characterization of compact metric spaces
6
1.6
Continuous functions
7-9
1.7-8
Normed linear spaces; linear operators, principle of uniform boundedness; contraction mapping principle
10
2.1-2
Topological spaces, subspaces
11
2.3
Continuous functions
12
2.4
Base for a topology
13
2.5
Separation axioms
14
2.6
Compactness
15
2.7
Locally compact spaces
16
2.8
Connectedness
17
2.9
Path connectedness
18
2.10
Finite product spaces
19-20
2.11-12
Transfinite induction; infinite product spaces, Tychonoff's theorem
21
2.13
Quotient spaces
22-23
3.1-4
Homotopic paths, fundamental group
24-25
3.5-6
Covering spaces; index of circle maps; applications of the index

Comments

Outline update: T. Gamelin, 5/96

NOTE: While this outline only suggests one midterm exam, it is strongly recommended that the instructor considers giving two. It is difficult to schedule a second midterm late in the quarter if it was not announced at the beginning of the course.
For more information, please contact Student Services, ugrad@math.ucla.edu.
 

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