Definition of compactness

The word "compactness" originated in the 16th century from the Latin words "compactus," meaning "pressed together" or "consecutive," and the suffix "-ness," which forms a noun. In mathematics, compactness refers to a property of a set that has no limit points outside the set itself. This concept was first developed by mathematicians like Carl Friedrich Gauss and Bernhard Riemann in the 19th century. In everyday language, compactness refers to something being condensed or packed tightly together, such as a compact suitcase or a compact city. The word has been used to describe various physical and abstract concepts, including mathematical sets, geometric spaces, and even social and economic systems. Over time, the meaning of compactness has expanded to encompass a sense of unity, cohesion, or density, while its mathematical roots remain an essential aspect of its definition.