Hint Use the definition of a closed set A set B in a metric

Hint: Use the definition of a closed set (A set B in a metric space M is said to be closed if its complement (that is, the set M \\ B) is open).

Solution

Consider point (1,0)S.

Note that if we take the -ball around this point, it will always include the point (1,/2)S^c.

This shows that S is not open.