ordinary topology, and the set of all positive rational numbers whose square is bigger than 2. Using the fact that is not in one can show quite easily that is a clopen subset of ( is not a clopen subset of the real line ; it is neither open nor closed in )

Properties

* A topological space is connected if and only if the only clopen sets are the empty set and itself.
* A set is clopen if and only if its boundary

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