Topology is the theory of shapes which are allowed to stretch, compress, flex and bend, but without tearing or gluing. For example, a square is topologically equivalent to a circle, since a square can be continously deformed into a circle. As another example, a doughnut and a coffee cup with a handle for are topologically equivalent, since a doughnut can be reshaped into a coffee cup without tearing or gluing.

As a starting exercise in topology, let's look at the letters of the alphabet. We think of the letters as figures made from lines and curves, without fancy doodads such as serifs.

**Question.**
Which of the capital letters are topologically the same, and which
are topologically different?
How many topologically different capital letters are there?