Lectures for Math 221a (topology), F17
I originally imagined writing a very short summary of each lecture.
I did not keep this up.
for what it's worth,
here is an incomplete outline of
most of what we covered and approximately when.
A topological space is a set of points
and a collection of "open sets"
that satisfy some axioms.
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.
The order topology,
the product topology,
and the subspace topology.
Closed sets, interiors and closures.
limit points and convergent sequences?
[((sub)basically) continuous functions?]
[Homeomorphisms and embeddings?]
[I lost count. We're up to section 2.8,
averaging exactly one section per lecture]
The product and box topology.
More about the product and box topology?
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)