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Bounded Set

A set S in a metric space (S,d) is bounded if it has a finite generalized diameter, i.e., there is an R<infty such that d(x,y)<=R for all x,y in S. A set in R^n is bounded iff it is contained inside some ball x_1^2+...+x_n^2<=R^2 of finite radius R (Adams 1994).

See also

Bound, Finite

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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.

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Bounded Set

Cite this as:

Weisstein, Eric W. "Bounded Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BoundedSet.html

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