 He made an important conjecture, only solved much later in 1982 by Pol and 1988 by Kimura, that the compactness degree was the same as the minimum dimension of a set that could be adjoined to the space to compactify it.Thus, for instance the familiar Euclidean space has compactness degree zero; it is not compact itself, but every point has a neighborhood bounded by a compact sphere.This compactness degree, zero, equals the dimension of the single point that may be added to Euclidean space to form its one-point compactification.