Bounded Set

A set  in a metric space  is bounded if it has a finite generalized diameter, i.e., there is an  such that  for all . A set in  is bounded iff it is contained inside some ball  of finite radius  (Adams 1994).

REFERENCES:

Adams, R. A. Calculus: A Complete Course. Reading, MA: Addison-Wesley, p. 707, 1994.

Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved Problems in Geometry. New York: Springer-Verlag, p. 2, 1991.

Jeffreys, H. and Jeffreys, B. S. "Bounded, Unbounded, Convergent, Oscillatory." §1.041 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 11-12, 1988.