Welcome to the wonderful world of topology!
Topology, more or less, is the study of spaces, or more specifically spaces where you can reasonably talk
about continuity and convergence. Topological spaces can be quite crazy, but we will figure out how to deal with them and understand when they are not so crazy. Some of the most basic questions we can ask are what do these
things look like? How many are there? How can we tell two of them apart? What interesting properties do they have?
Among other things we will see how to recognize nice spaces from minimal data, prove that "Cantor dust" can block out all light from the sun, show that a 2 dimensional square is the continuous image of a small line segment, and construct nowhere differentiable functions.
- Since we are covering surfaces differently from the book I am posting my lecture notes (this does not follow the class lectures precisely but is fairly close): Set 1, Set 2 and Set 3.
- The due date for Homework 5 is now November 24th.
- The due date for Homework 4 is now November 3rd.
- The first class will be August 20 (I will be out of town on the 18th).