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A. A set is uncountable if its derived set is uncountable.
B. Derived set of an uncountable set is uncountable.
C. Non empty interior set of a set is open. D. All of the above.
This is a multiple select question.

I considered a Set of Rational no., Now its derived set is R(Set of Real numbers) which is uncountable, but the set of rational numbers is countable.So option A must be false,Right?
Option B is true, if i take set of irrational numbers, which is uncountable and its derived set is R which is again uncountable.
How should i proceed option c?
Also What all are the property of derived sets?

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    What is a derived set? – 2017-01-28
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    derived set is the set of all limit points of a set – 2017-01-28
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    Are you considering only subsets of the real numbers (with the standard metric) or all metric spaces? – 2017-01-28

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