# Difference between revisions of "Approximately-compact set"

A set having the property of approximate compactness. A metric projection on any approximately-compact Chebyshev set is continuous. Examples of approximately-compact sets include boundedly-compact sets and closed convex sets in the spaces $L_p$ ($0<p<\infty$), and the set of rational fractions in which the degrees of the numerator and denominator are constant. In approximation theory and in the theory of ill-posed problems frequent use is made of spaces in which all closed sets are approximately compact.