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 * S is neither open nor closed in R S is clopen in R S is open but not closed...

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

Jun 04, 2022

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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 * S is neither open nor closed in R S is clopen in R S is open but not closed...

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