Definition of a continuous function (through open sets) Why the definition of a continuous function defined in terms of inverse function? 
$f$ - continuous function, if for every open $V$, $f^{-1}(V)$ is open. 

Because it is easier to use than the regular caculus like definition,
f is continuous iff for all x and open V nhood f(x), there be an open U nhood of x with f(U) subset V.   
The two defintions can be proven equivalent.
The later for real to real functions can be be shown equivalent to the usual epsilon delta definition.  Likewise, for R^n to R functions.
