Answer by NKS for For an $n$-dimensional object, how many types of holes are...
I think Alexander Duality is what you are looking for. I gather that you are a non-expert, so I will attempt to describe in fairly informal terms how Alexander duality deals with the questions that you...
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For an $n$-dimensional object, how many types of holes are possible?
Update 2012-06-06: At some point I'll attempt to answer my own question by using a dual-fluid model that places the dimensionality and connectivity of "solids" and "holes" on an equal footing. With...
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