Fractal Dimension of Graphs of Typical Continuous Functions on Manifolds

If M is a compact Riemannian manifold and C(M, R) is the set of all real valued continuous functions defined on M, then we show that for typical element f is an element of C(M, R), (dim) over bar (B) (graph(f)) is as big as possible and for typical f is an element of C(M, R), (dim) under bar (B)(graph(f)) is as small as possible.