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State whether each of the following sets are open, closed, both, or neither: (1) In Z with the finite complement topology: {0, 1, 2), {prime numbers), {n | |n| 2 10}. (2) In R with the standard topology: (0, 1), (0, 1], [0, 1], {0, 1}, {1/n | ne N]. (3) In R2 with the standard topology: {(x, y) | x2 + y? = 1], {(x,y) | x2 + y> > 1], {(x, y) | x2+ y2 21}.

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State whether each of the following sets are open, closed, both, or neither:
(1) In Z with the finite complement topology: {0, 1, 2), {prime numbers), {n | |n| 2 10}.
(2) In R with the standard topology: (0, 1), (0, 1], [0, 1], {0, 1}, {1/n | ne N].
(3) In R2 with the standard topology: {(x, y) | x2 + y? = 1], {(x,y) | x2 + y> > 1],
{(x, y) | x2+ y2 21}.

 
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