👉 In compactness, a mathematical object or concept is said to be "incompact" if it can be expressed as a finite union of sets that are all smaller than itself. This means that each set within an incompact object must contain at least one element that is not contained within another set within the same object. In other words, every subset of the object can be made into a proper subset by removing some elements from it without introducing new ones. For example, consider the concept of "in