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?