Product Topology

I use this activity to really drive home what the product topology is and how we think about the open sets.

Timing

• Prep time: 30 minutes or so
• Class time: 20 minutes or so
• Curriculum location: After introducing product topologies

Supplies

Quantities depend on the number of students in your class.

• Children's inner tubes such as these, one per group
• An air pump or strong lungs
• Whiteboard markers, 1-2 per group
• This worksheet
• LaTeX file
• s1.pdf
• Rubbing alcohol

Instructor Instructions

Preparation

1. Blow up the inner tubes
2. Print and make copies of the worksheet

In Class

1. Remind students of the definition of the product topology, and how we can use it to form the torus.
2. Hand out the worksheet, inner tubes, and whiteboard markers and do your group work thing!

After Class

1. Immediately after class, clean the inner tubes. If the ink sticks, use the rubbing alcohol to get it off.