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manifold vs. function

highmath

Member
Sep 24, 2018
36
(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
Jan 30, 2018
344
It's not clear to me what you are asking. A manifold is a set of points in [tex]R^n[/tex] and a function is not. A function may have a graph that is a manifold. For example, the graph of [tex]z= x^2+ y^2[/tex] is a parabola so 2 dimensional manifold in [tex]R^3[/tex]. On the other hand, a sphere is a manifold while [tex]x^2+ y^2+ z^2= r^2[/tex] is NOT a function.

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