(adsbygoogle = window.adsbygoogle || []).push({}); Changes in the internal structure during a "Topological transform"

Is there any field of topology which deals with the changes in internal structure of an object when it undergoes topological transform? If I'm transforming a cube in to a sphere, is there any 'field of topology' which analyze the structural changes inside the cube. For example, in what way does the points defining the cube get affected. Can you please recommend me some books regarding this. Thanks in advance.

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# Changes in the internal structure during a Topological transform

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