# manifold vs. function

#### highmath

##### Member
(1) What the differences between manifolds to function?
(2) Is there an example to manifold that is not a function?
(3) Is there function that is not manifold?

#### Country Boy

##### Well-known member
MHB Math Helper
It's not clear to me what you are asking. A manifold is a set of points in $$R^n$$ and a function is not. A function may have a graph that is a manifold. For example, the graph of $$z= x^2+ y^2$$ is a parabola so 2 dimensional manifold in $$R^3$$. On the other hand, a sphere is a manifold while $$x^2+ y^2+ z^2= r^2$$ is NOT a function.

Could you clarify- what definitions of "manifold" and "function" are you using?