MHB Progress and Accomplishments: A Look at What's Been Done

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Uniman said:
https://www.physicsforums.com/attachments/425

It is necessary to remember that in a point $t_{0}$ where f(t) isn't continous, the Fourier Series converges to... $\displaystyle S_{0} = \frac{1}{2}\ \{\lim_{t \rightarrow t_{0} +} f(t) + \lim_{t \rightarrow t_{0} -} f(t) \}$ ... under the assumption that both limits exist...

Kind regards

$\chi$ $\sigma$
 
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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