Let R (the set of real numbers) be equipped with the Euclidean topology and let S be the set of all irrational numbers. Then * S is closed but not open in R S is neither open nor closed in R S is open...

Let R (the set of real numbers) be<br>equipped with the Euclidean<br>topology and let S be the set of all<br>irrational numbers. Then *<br>S is closed but not open in R<br>S is neither open nor closed in R<br>S is open but not closed in R<br>O S is clopen in R<br>O O<br>

Extracted text: Let R (the set of real numbers) be equipped with the Euclidean topology and let S be the set of all irrational numbers. Then * S is closed but not open in R S is neither open nor closed in R S is open but not closed in R O S is clopen in R O O

Jun 04, 2022

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Let R (the set of real numbers) be equipped with the Euclidean topology and let S be the set of all irrational numbers. Then * S is closed but not open in R S is neither open nor closed in R S is open...

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