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Let be a cellular map, and let be a point different from such that and.
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Since is a cellular map, is well defined and is also a cellular map.
Then, is a cellular map homotopic to and.
Then, there is a cellular map homotopic to such that.
Then, there is a cellular map such that and.
There is a cellular map such that and.
Then, by Lemmas 5.1 and 5.2, for each, there is a cellular map such that and.
Moreover, we say that is of type if in addition we can choose the map being a cellular map.
Since is a cellular map, the 1-skeleton of is carried by into the 0-cell of.
Your research specialty is a cellular function called protein folding.
Moreover, is carried by (which is also a cellular map) into the 0-cell of the sphere, for all.
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