In: Advanced Math
Previously, we listed all 29 topologies on the set X={a,b,c}. However, some of the resulting topological spaces are homeomorphic. Which are homeomorphic? Divide the set of 29 topological spaces into homeomorphism classes, and be sure to justify your choices. There are 9 homeomorphism classes in total. (To justify your choices, explain why the spaces within each class are homeomorphic to each other. Your explanations can be somewhat loose).