The role of topology in engineering design research

Aspects of the mathematical specialty of topology appear within several seemingly distinct areas of engineering design and engineering design theory. Indeed, the expression topology of a design is often used informally. In this article a primary intent is to demonstrate the diversity of applications of topology within engineering design. A complementary goal is to introduce the engineering design community to topology as a rich, formal, well-established mathematical discipline that may be of value for wider study. Upon reviewing some of these topological applications, it appears that topology holds promise as a basis for formalizing engineering design theory. This article considers topology as a basis for unifying design abstractions. The potential benefit may be the realization of commonalities between design aspects previously considered separately, where each now has its own attendant specialized, expensive analyses.