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 * O Sis open but not closed in R O s is closed but not open in R ) Sis neither...


Let R (the set of real numbers) be equipped with the Euclidean topology and let S<br>- (0, 1, 1/2, 1/3, ., 1/n, ...}, Then *<br>O Sis open but not closed in R<br>O s is closed but not open in R<br>) Sis neither open nor closed in R<br>S is clopen in R<br>

Extracted 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 * O Sis open but not closed in R O s is closed but not open in R ) Sis neither open nor closed in R S is clopen in R

Jun 04, 2022
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