Does there exist in Euclidean 3-dimensional space R^3 a continuous 
2-dimensional surface S specified by an equation of the form z=f(x,y),
which satisfies the following conditions?

(1) f is continuous at each point (x,y) belonging to some non-empty connected
open subset of the x-y plane.
(2) Given any arc c on S, c has no tangent at any of its points (or even no
half-tangent at any of its points)