The operation of intersecting lines inside a geometric figure, which is accomplished by inter-connecting the vertices, is resolved into a determined set of constitutive fragments, these being geometric figures themselves. Thus, computing the area by either of these two operations yields the same value. The two operations for resolving the area bounded by the four points are therefore functionally equivalent. Labeling inter-sections is a mathematical operation that involves the specification of the topological features of the defined arrangements of points. In Ethnosemantics, the topological manifold is defined as an ethnosemantic outline .
Ethnosemantic outlines are topological arrangements of topic domains.
These topic domains thus correspond to topological fields or spaces whose empirically derived dimensionality and interconnectivity characterize exactly the notion of ethnic group or ethnicity. Labeling intersections in ethnosemantic outlines amounts to the operation topic fragmentation . Topic fragmentation re-solves into labeled topical constituents called deictic topic nominals . These are fixed in form and number and correspond to the labels of geometric figures. A powerful nationality etc.