# 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 $d(x,y)\leq M$ whenever $x,y\in A$.

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

Title bounded Bounded 2013-03-22 12:05:11 2013-03-22 12:05:11 PrimeFan (13766) PrimeFan (13766) 12 PrimeFan (13766) Definition msc 54E35 TotallyBounded AlternateStatementOfBolzanoWeierstrassTheorem