- #1
saminator910
- 96
- 1
I am having trouble getting a set definition of what constitutes a manifold for example ,
I have the real plane R^2, and the sphere
s = {(x,y,z)|(x,y,z)£R^2, x^2+y^2+z^2=1}
Note £, is meant to be "element of".
And I have a continuous function f mapping the real plane onto s such that
f:R^2-->S
Is S considered a manifold?, please tell why or why not and I really need some examples of manifolds, and how one defines its structure . Oh and I know whole courses are taught on this, but, I appreciate any response
I have the real plane R^2, and the sphere
s = {(x,y,z)|(x,y,z)£R^2, x^2+y^2+z^2=1}
Note £, is meant to be "element of".
And I have a continuous function f mapping the real plane onto s such that
f:R^2-->S
Is S considered a manifold?, please tell why or why not and I really need some examples of manifolds, and how one defines its structure . Oh and I know whole courses are taught on this, but, I appreciate any response