|
The question must have been about "homeomorphic" not "homomorphic":
It's a topology question.
C is homeomorphic to N, S and U since all four of these letters can't
be straightened out to (are homeomorphic to) a line segment.
C is not homeomorphic to J because if we take away the top middle point
of the J we are left with three connected components, while this cannot
happen with any point of C. (Using: If X is homeomorphic to Y and x is
element of X and y is element of Y then X-{x} is homeomorphic to Y-{y}.)
C is not homeomorphic O because the latter has a loop in it that can't
be shrunk to a point in it. (Technically, they have different fundamental
groups -- not a concept that would be on the GRE.)
|