ABSTRACT
Given a division 1C of K let JCc be the set of all (Ic, t + c) such that (I, t ) belongs to K. Show that if JC is an a-division of K then Kc is a /3-division of K. (Existence of such a for a given β on K holds for any orientation-preserving, topological transformation of K. Translations are a special case of such transformations. It is only for K of dimension 1 that cells, tagged cells, figures, partitions, and divisions in K are purely topological entities. These structures in higher dimensions depend upon the ordering in Rn .)
§1.3 T he U p p er and Lower In teg ra ls o f a S um m ant over a F igure.
