bounded

Given a metric space $(X,d)$, a subset $A\subseteq X$ is said to be bounded if there is some positive real number $M$ such that $d(x,y)\le M$ whenever $x,y\in A$.

A function $f:X\to Y$ 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