Given a metric space (X,d), a subset AX is said to be bounded if there is some positive real number M such that d(x,y)M whenever x,yA.

A function f:XY from a set X to a metric space Y is said to be bounded if its range is bounded in Y.

Title bounded
Canonical name Bounded
Date of creation 2013-03-22 12:05:11
Last modified on 2013-03-22 12:05:11
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 12
Author PrimeFan (13766)
Entry type Definition
Classification msc 54E35
Related topic TotallyBounded
Related topic AlternateStatementOfBolzanoWeierstrassTheorem