For example, consider an annulus in $R^2$. It has a hole in the middle, but is otherwise connected. What is the proper classification of this topological object?
What is the proper topological term for a region with a single hole?
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general-topology
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0It might help if you are a bit more clear about what you mean when you say "region." Are you interested only in regions inside Euclidean space? – 2012-12-11
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0Non-simply connected? – 2012-12-11
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0I think there are lots of topological ways to describe this difference between a disc and an annulus. Most of them will not be equivalent when applied to more complicated situations. – 2012-12-11
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0Maybe the Euler characteristic would be useful? I really don't know anything about this but I think that if the set is nice enough you can triangulate it and the Euler characteristic will tell you how many holes it has. – 2012-12-12