Let $X$ be an infinite set with its cofinite topology. I was asked to mention the clopen sets. I think the only clopen sets are X and the empty set, because otherwise, if A is a clopen set, it would mean that both A and its complentary set are finite, so their union, which is X, is finite - a contradiction. Am I right? Thank you!
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6Yes, you are right (and maybe should have more faith in your mathematical skills). – drhab Jun 21 '17 at 07:23