Topology deals with geometric properties that are
dependent only on the relative positions of the components
of figures and not on such concepts as length, size, and
magnitude. Topology supports design and representation
of mechanical devices, communication and transportation
networks, topographic maps, and planning and controlling
of complex activities. In addition, aspects of topology
are closely related to symbolic logic, which forms the
foundation of artificial intelligence. By approaching engineering
design from this abstract point of view, it is possible
to use topological methods to study collections of geometric
objects or collections of entities that are of concern
in design analysis or synthesis. The importance of topological
representation and reasoning in analysis, design, and manufacturing
is heightened by the contemporary view that stresses the
need for conceptual design.