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Math Help - topology epsilon-delta definition of continuity

  1. #1
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    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?
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  2. #2
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    \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)
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