Compactness refers to the property of an object or space being closely packed or dense, minimizing empty areas. In mathematics, particularly in topology, a set is considered compact if it is both closed and bounded, meaning it contains all its limit points and fits within a finite space. This concept is crucial for various mathematical proofs and theorems. In everyday life, compactness can describe physical objects, such as a compact car designed to occupy less space while still providing functionality. Compactness is often valued in design, as it allows for efficient use of space, making items easier to store and transport.