The definition of open set is that every point in set A is an interior point. For the set of rational numbers Q, take any point R in Q, because both rational numbers and irrational numbers are dense on R, it is impossible to find a neighborhood (a, b) of R, so that any point in (a, b) belongs to Q (that is, any neighborhood of rational numbers has irrational numbers), and R is not an interior point. There are usually different definitions for closed sets. An equivalent definition is that the set A satisfies the condition that a' is contained in a, where a' represents the set of all limit points of A, which is called the derivative set of A. Look at the rational number set Q, a series of numbers r 1, r2...rn is taken from Q, and the limit of this rational number sequence {rn} is not necessarily rational (fact. For example, the limit 1, 1, 4,1.41.414 ... is irrational √2, so q' cannot be included in q, so q is not closed. If you don't understand, please ask.