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This report explains how to factor partial orders to get quotient partial orders and how to factor cpo-s to get quotient cpo-s. This is supplemented by an important issue of collapsing the cpo-s to simpler ones. The motivations for this research come from investigations of concurrent processes addressed elsewhere. However, the article may be read independently of these motivations.
It is shown that if X is a compact 2-dimensional polyhedron and if f is a mapping of X to a surface M, then f x id[sub Ik] (f x id[sub Sk], respectively) is essential for every [k is greater than or equal to 0] if and only if each T-modification of f is essential.
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