Topologically Distinct – holier than thou

A necessary (but not sufficient) criteria
for two surfaces to be topologically equivalent is that they have the same
number of “holes”. So if one surface is “holier”
than “thou” (another), then they would be topologically distinct.

http://en.wikipedia.org/wiki/Topology

http://mathworld.wolfram.com/Topology.html

http://en.wikipedia.org/wiki/Homeomorphism

http://mathworld.wolfram.com/Homeomorphism.html

Note:
Be careful not to confuse “homomorphism” and “homeomorphism”.