Wow - I took introductory topology with Colin just a few years ago. He wove in a few examples from OP's book and I had several friends who took his knot course - excellent resource for anyone interested and he is an amazing person/mathematician.

Readers here might appreciate one of my favorite homework "problems" from his topology course- it's a simple but counter-intuitive mathematical result that's easy to replicate even for young children. Rip a sheet of paper (8.5x11 will do) in two long strips. Take the strips and tape them so that one is a ring and the other is a Moebius strip.

Here's where the magic happens: make a guess about what happens when you cut each object long-ways, then cut both objects with a pair of scissors. Won't give any spoilers but the result may surprise you :)

EDIT: also forgot to mention the knot book and his topology book are great at highlighting open/outstanding problems that precocious undergrads could tackle. I definitely wish more authors of math texts went out of their way to point out avenues for exploration like this.