👉 In mathematics, a semiclosed set is a subset of a larger set that is not closed under all operations. It can be defined as a set that is both open and closed at the same time. For example, if A is an infinite set and B is any subset of A, then B is said to be a semiclosed set if it contains infinitely many elements from A. In other words, a semiclosed set is a set that can be both open (i.e.,