Quotient Topology 2

This is another exercise I use to help my students understand quotient topologies. This time, I'm getting them to understand what we mean by open sets under the quotient topology.

Timing

• Prep time: Less than an hour
• Class time: 20 minutes or so
• Curriculum location: After introducing quotient topologies

Supplies

Quantities depend on the number of students in your class.

• Colored paper, 1-3 sheets per group
• Scissors or paper cutter
• This worksheet
• LaTeX file
• ixi.pdf

Instructor Instructions

Preparation

1. Cut the paper into strips as thick as you can make them while also forming a Mobius strip.
2. Print and make copies of the worksheet

In Class

1. Remind students of the definition of the quotient topology. Also remind/show them what an annulus/mobius strip is.
2. Hand out the worksheet and do your group work thing!

Note: you could easily reenvision this to be done entirely in 2D by using a different quotient space.