For each of the following statement, indicate whether it is true or false. Suppo

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For each of the following statement, indicate whether it is true or false. Suppose that A is a subspace of X and that B is a subset of A that is closed in subspace topology. Then B is a closed subset of X. Suppose that G is an open subset of X and that U is a subset of G that is an open subset of G in the subspace topology. Then U is an open subset of X. Any subspace of a connected space is connected. Any quotient space of a connected space is connected. Any closed subset of X times Y is of the form A times B where A is a closed subset of X and B is a closed subset of Y. Let A be a closed subset of R2 and let S = {x: (x, y) A for some y R}. Then S is a closed subset of R. (Assume that R2 and R both have their usual topologies.) Let A be an open subset of R2 and let S = {x : (x,y) A for some y R}. Then S is an open subset of R. (Assume that R2 and R both have their usual topologies.) If we remove one point from a space, the resulting space is never homeomorphic morphic to the original space.

Explanation / Answer

1 T 2 F 3 T 4 F 5 F 6 T 7 F 8 T

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