# Compact set

This has a general meaning in mathematical analysis. For mathematical programming, where we work in finite-dimensional Euclidean vector spaces, it means the set is closed and bounded. This is often an assumption about the feasibility region in order to ensure the existence of an optimum value for a continuous objective function – see Weierstrass' theorem. Any finite set is compact. An open interval $LaTeX: (a,b)$ is not compact because its endpoints, $LaTeX: a$ and $LaTeX: b$ are limit points but are excluded from the set.