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).
Bounded Set
See also
Bound, FiniteExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Bounded SetCite this as:
Weisstein, Eric W. "Bounded Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BoundedSet.html