A (symmetrical) boundary set of radius r and center x_0 is the set of all points x such that left bracketing bar x - x_0 right bracketing bar = r. Let x_0 be the origin. In R^1, the boundary set is then the pair of points x = r and x = - r. In R^2, the boundary set is a circle. In R^3, the boundary set is a sphere.

circle | compact set | disk | open set | sphere