TIFR-2015-Maths-B-1

Question

Let $X$ be a proper closed subset of $[0, 1]$. Which of the following statements is always true?

• A. The set $X$ is countable.
• B. There exists $x \in X$ such that $X$ \ $\left \{ x \right \}$ is closed
• C. The set $X$ contains an open interval.
• D. None of the above.

Comments

What option B says here ??

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set minus notation.