Topology Review

I would argue that point-set topology is all about telling which topological spaces are homeomorphic, and which are not. So, at the end of the semester I had my students take a bunch of topological spaces and sort them into equivalence classes.

Timing

• Prep time: 30 minutes or so
• Class time: 20 minutes or so
• Curriculum location: End-of-semester review

Supplies

• A paper cutter or scissors
• Business-size envelopes, one per group
• This worksheet
• LaTeX file
• 4-5-topsine.png
• 4-6-cantor.png
• 4-6-d2.png
• 4-6-s1.png
• 4-6-square.png
• 4-6-topcomb.png
• 4-6-wedge.png

Instructor Instructions

Preparation

1. Print and make copies of the worksheet
2. Cut the worksheets to separate the topological spaces. Be sure to keep the images with their respective spaces.
3. Put one complete set into each envelope.

In Class

1. Tell the students that their objective is to sort the spaces into homeomorphic equivalence classes. They should be able to (verbally) prove that their answers are correct.
2. Hand out the envelopes and do your group work thing!