Adjectives Review

Point-set topology is full of adjectives, and they can be hard to keep track of. Topology is also full of a lot of fun examples and counterexamples. I used this as a review exercise after spring break to help my students remember all the words we had discussed.

Timing

• Prep time: The speed of your printer
• Class time: 20 minutes or so
• Curriculum location: As a post-break review or end-of-semester review

Supplies

• This worksheet

Instructor Instructions

Preparation

1. Print and make copies of the worksheet

In Class

1. Remind students of the definitions of compact, Hausdorff, connected, and metrizable. Note that there are some theorems that say one implies the other, and also some theorems that we haven't covered yet!
2. Their task is to fill in the Venn diagram with topological spaces. Point out to them where the boundaries are to each region.
3. Hand out the worksheet, and do your group work thing! Remind students that it's not possible to fill in all 16 blanks.
4. At the end of the activity, go through all the answers the class generated. Point out which theorems you've covered that say some boxes cannot be filled in.

Note: You can make this feel more tactile by, instead of having students generate their own examples, printing examples and cutting them into tiles, then having the students place the tiles in the appropriate place on the Venn diagram.