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is that there are two components, each contractible (Schoenflies theorem, to be accurate about what is used here). That is, the correct answer in honest Betti numbers is

:2, 0, 0.

Once more, it is the reduced Betti numbers that work out. With those, we begin with

:0, 1, 0

to finish with

:1, 0, 0.

From these two examples, therefore, Alexander's formulation can be inferred: reduced Betti numbers are related in

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