Let R (the set of real numbers) be equipped with the Euclidean topology and let S = {0, 1, 1/2, 1/3, ..., 1/n, ...}. Then * %3D O Sis clopen in R S is closed but not open in R O S is neither open nor closed in R O sis open but not closed in R

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topology
Let R (the set of real numbers) be equipped
with the Euclidean topology and let S = {0, 1,
1/2, 1/3, ..., 1/n, ...}. Then *
%3D
O Sis clopen in R
S is closed but not open in R
O S is neither open nor closed in R
O sis open but not closed in R
Transcribed Image Text:Let R (the set of real numbers) be equipped with the Euclidean topology and let S = {0, 1, 1/2, 1/3, ..., 1/n, ...}. Then * %3D O Sis clopen in R S is closed but not open in R O S is neither open nor closed in R O sis open but not closed in R
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