Lectures for Math 221a (topology), F17
I originally imagined writing a very short summary of each lecture.
I did not keep this up.
However,
for what it's worth,
here is an incomplete outline of
most of what we covered and approximately when.

9/29:
A topological space is a set of points
and a collection of "open sets"
that satisfy some axioms.

10/2:
There are many definitions of "basis".
The idea is to take just some of the open sets
and make the rest by taking unions.
A subbasis is similar,
but you can also use intersections.

10/4:
The order topology,
the product topology,
and the subspace topology.

10/6:
Closed sets, interiors and closures.

10/9:
Hausdorff spaces,
limit points and convergent sequences?

10/11:
[((sub)basically) continuous functions?]

10/13:
[Homeomorphisms and embeddings?]

10/16:
[I lost count. We're up to section 2.8,
averaging exactly one section per lecture]
The product and box topology.

10/18:
More about the product and box topology?

10/20,23,25:
Metric spaces.

10/27: The quotient topology.

...: compactness and connectedness.

11/27: There are two weeks left to cover:
 the rest of Chapter 3 (limit point compactness, local compactness)
 Chapter 4 (countability axioms and Urysohn)
 Chapter 5 (Tychonoff and stuff)
 Chapter 6? (paracompactness and stuff)
 Chapter 7? (completeness, compact metric spaces, Ascoli, Baire)
Prof. Bigelow
20171204