Why singleton set is open in Q but is open in Z?

In the standard topology on the rational numbers ( \mathbb{Q} ), a singleton set ( {q} ) is not open because you cannot find a rational interval around ( q ) that contains only ( q ) and no other points from ( \mathbb{Q} ). In contrast, in the topology on the integers ( \mathbb{Z} ), which is discrete, every singleton set ( {z} ) is open because every integer is isolated from others, allowing us to form an open set containing just that integer. Therefore, singleton sets are open in ( \mathbb{Z} ) but not in ( \mathbb{Q} ).