10. Consider the set of integers Z. For each n € Z we define the set B(n) = {n} if n is odd and B(n) = (n − 1, n, n + 1} if n is even. The collection B = {B(n) n|ne E Z} is a basis for a topology on Z. The resulting topology is known as the "digital line topology" and we refer to Z with this topology as the "digital line". Show that the digital line is not homeomorphic to Z with the finite complement topology.

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