We need to understand topology as well. How are simple elements joined, and how do we preserve these attachments when we transform the model? Topological properties are not metrical; they concern connectivity and dimensional continuity. These are the things that when transformed stretched, bent, twisted, or compressed without tearing, puncturing or inducing self-intersections still persist unchanged. Much of what the hemocoel does has to do with the topology of closed paths, piecewise flat surfaces, and closed curved surfaces. Ultimately physiologists and biologists will have to acquaint themselves with such formulations as the closed-path theorem, and the Jordan curve theorem.

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