Consider the English alphabet in this font with serifs
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Consider any letter in this font as a topological space (assume that letters don't have weight and are genersted by lines) and consider a continuous mapping from any letter to itself. For which letters any such mapping have a fixed point and for which it has not? For O the answer is negative, for C, Z, S it is positive.
The main difficulty for me is serifs. For the sans-serif font like Arial the problem is much easier. Here we can't even easily divide letters into topologically equal groups and these groups aren't obvious: G ~ J, T ~ I ~ U ~ W, E ~ F, C ~ Z ~ S etc.