Math 445: Introduction to Topology I
University of Illinois at Chicago
||Topology, 2ed by James R. Munkres. (Prentice Hall, 2000)
UIC library / Google books / Amazon
MWF at 1pm in 309 Taft Hall
Instructor office hours
39509 (undergraduate), 39510 (graduate)
About the course
Math 445 provides an introduction to topology, which is the field of
mathematics concerned with a formalization of the notion of
"shape". Most of the course will focus on the area within
topology known as point set topology. We will define topological
spaces and discuss some important examples, such as metric spaces. We
will study a variety of properties of topological and metric spaces,
including compactness and connectedness. We will also discuss general
methods for constructing new topological spaces from existing ones,
such as products, quotients, and subspaces.
We will cover chapters 2–4 in the textbook and selected topics from
Calendar & Grading
This is a condensed summary of some important dates and the weights
used to compute your course grade. The course syllabus is the
definitive reference for course policies.
||Course grade fraction
||Most Mondays (see list below)
||Wed Mar 6
||Mon May 6
Problem sets and their due dates are listed below. Unless otherwise noted on the assignment, homework is due in class
at the beginning of the lecture (i.e. at 1:00pm in 309 Taft Hall).
- Homework 0 due Friday January 18: Read the syllabus
- Homework 1, due Monday January 28
- Homework 2, due Monday February 4
- Homework 3, due Monday February 11:
Problems 17.11, 17.13, 18.2, 18.4, 18.7, and 18.10 from Munkres
- Homework 4, due Monday February 18
- Homework 5, due Monday February 25
Typeset solutions are not required. If writing solutions by hand,
please make sure they are legible. Staple homework if it spans
several sheets of paper. Write your name and the assignment
number (e.g. "Homework 1") at the top of the first page.
Many of the homework problems are assigned directly from the primary textbook (Munkres, 2ed).
Lecture titles and textbook sections
- Lecture 1 (Mon Jan 14): Topologies and topological spaces (§13)
- Lecture 2 (Wed Jan 16): The topology determined by a basis (§13)
- Lecture 3 (Fri Jan 18): Recognizing a basis of a topology, comparing topologies (§13)
- Lecture 4 (Wed Jan 23): The product topology (§15)
- Lecture 5 (Fri Jan 25): The subspace topology (§16)
- Lecture 6 (Mon Jan 28): Closed sets and limit points
- Lecture 7 (Wed Jan 30): (class canceled due to weather)
- Lecture 8 (Fri Feb 1): T1 and T2 spaces (§17)
- Lecture 9 (Mon Feb 4): Continuity (§18)
- Lecture 10 (Wed Feb 6): Homeomorphisms, embeddings, examples of continuous functions (§18)
- Lecture 11 (Fri Feb 8): Criteria for continuity, pasting lemma (§18)
- Lecture 12 (Mon Feb 11): Box and product topologies (§19)
- Lecture 13 (Wed Feb 13): Box and product topologies (continued) (§19)
- Lecture 14 (Fri Feb 15): The metric topology; metric space examples (§19)
- Lecture 15 (Mon Feb 18): Metrics on RJ (§19); ε-δ continuity (§20)
- Jan 14: Chapter 2 (and skim Chapter 1)
For students looking for another place to read about the topics from the course, I recommend:
- Topology by Klaus Jänich, Springer, 1984.
- Chapters 1, 3, 4, 6, 8, and 10 contain material we will cover in math 445.
- Introduction to Topology, 2ed by Theodore Gamelin and Robert Greene, Dover, 1999.
- This book is terse but clearly written. It begins by discussing the topology of metric spaces in some detail, introducing general topological spaces a bit later.
- Chapters 1 and 2 contain material we will cover in math 445.
Students who are learning TeX / LaTeX and who want to typeset their homework may find this template helpful: