Possible Duplicate:

Function with range equal to whole reals on every open set

Hello,

My problem is the following "Is there a Real valued function with image of every open interval the whole real line?. Shall it exist, construct it"

I know so far that this equals finding uncountably many dense disjoint subset of R (in particular the preimages of the elements of R).

I shall be jolly thankful to anybody with a clue.