# topology epsilon-delta definition of continuity

• February 22nd 2009, 10:47 PM
tomboi03
topology epsilon-delta definition of continuity
Prove that for functions f: R -> R, the epsilon-delta definition of continuity implies the open set definition

I have this written down.
A function f from R to R is continuous at a point p E R (p in R) if given epsilon>0 there exists delta>0 such that if |p-x|<delta then |f(p)-f(x)|< epsilon.

I don't know where to go from there...
Can someone help me out?
• February 23rd 2009, 03:10 AM
Plato
$\left\{ {x:\left| {x - p} \right| < \delta } \right\} \equiv \left( {p - \delta ,p + \delta } \right)\;\& \,\left\{ {f(x):\left| {f(x) - f(p)} \right| < \varepsilon } \right\} \equiv \left( {f(p) - \varepsilon ,f(p) + \varepsilon } \right)$