## Math 430 |

Topology is the abstract study of *continuity*.
What are the basic structures one needs to talk rigorously about a function
from one set to another (or itself) being continuous?

In Topology, once continuity is understood, we classify
sets (really topological spaces) by asking if there is a continuous
bijection with continuous inverse between them. If so, we say they are
*homeomorphic*.

The textbook gives an elementary introduction to topology, but allows the student to see the beginnings of each of the three major branches of topology, namely, point-set topology, algebraic topology and differential topology.

Topology is not just for theorists anymore. Major and surprising applications exist. In some sense the field of differential equations is a subset of differential topology. Algebraic topology is used in everything from general relativity to the mathematics of robotic systems. Point-set topology is now used in computer science and chaos theory.

**Textbook:** *A Combinatorial Introduction to Topology* by Michael Henle

**Grades:** Homework 30%, midterm 30%, final 30%, class presentations 10%

**Hwk Set #1.**

pg 14: 2, 4

pg 19: 7, 8, 9**Hwk Set #2.**

pg 25: 6

pg 27: 10, 11, 12, 15

**Hwk Set #3.**

pg 46: 1c, 1f, 2

pg 48: 5

pg 53: 1b, 1c, 2a

pg 58: 6

pg 60: 9

You may use a computer for the vector fields.**Hwk Set #4.**

pg 87: 1, 4

pg 89: 2, 3, 4, 7

pg 90: 11

pg 95: 3

pg 100: 2**Hwk Set #5.**

pg 109: 4ad

pg 113: do 5 but do not turn in, 6

pg 115: 10, 11ac

pg 120: 5ab

pg 122: 8d

pg 124: 3i

pg 128 4i, 5

pg 131: 1b

(Due one week after we finish Chapter 4.)