What is the Cauchy Product Formula in Power Series?

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Rudin motivates this formula by multiplying two power series and then setting z = 1 and somehow obtaining the cauchy product formula. But I am not following how he does this at all. Can anyone help me understand this?
 
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Nevermind I figured it out!
 

Thread '2-sphere intrinsic definition by gluing disks' boundaries'

A sphere as topological manifold can be defined by gluing together the boundary of two disk. Basically one starts assigning each disk the subspace topology from ##\mathbb R^2## and then taking the quotient topology obtained by gluing their boundaries. Starting from the above definition of 2-sphere as topological manifold, shows that it is homeomorphic to the "embedded" sphere understood as subset of ##\mathbb R^3## in the subspace topology.
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