Discussion of Exercise 6 of Section 1.4:
Homeo, homeo, wherefore art thou homeo?

Dr. Jorge Alberto Calvo of Ave Maria University in Florida writes:

I am using your textbook for my knot theory course. So far, I am enjoying it tremendously.

However, I have a question: What is the solution to Exercise 6 in Section 1.4?

Just curious . . .  Jorge

Robert Messer replies:

In Shakespeare's original version, Juliet answers her own question:

'Tis but thy name that is my enemy:
Thou art thyself, though not a Montague.
What's Montague? It is nor hand nor foot,
Nor arm nor face, nor any other part
Belonging to a man. O be some other name!
What's in a name? That which we call a rose
By any other word would smell as sweet;
So Romeo would, were he not Romeo call'd,
Retain that dear perfection which he owes
Without that title. Romeo, doff thy name,
And for thy name, which is no part of thee,
Take all myself.

I suppose your students could adapt that to explain the term "homeomorphism" as well!

Phil Straffin adds:

In case your students find Bob's poetic response stirring but unclear, the problem can be interpreted as asking for a proof that the composition of two homeomorphisms is a homeomorphism. Some of my students didn't get it either! But those that got it did enjoy it.