Generically, top sets should be points, but they can also be curves or regions, as for example, in polyhedral surfaces, edges and faces are top sets for some directions. It is also possible for more complicated sets to be top sets, including sets that are not simply connected, and even sets that are not embeddings.
Top sets of surfaces in three-space always lie in a plane.
Top sets play a crucial role in the study of tightness.
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The Geometry Center