I am having trouble getting a set definition of what constitutes a manifold for example ,(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Confused as to what constitutes a manifold?

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