Sets of uniqueness and systems of inequalities having a unique solution
J. H. B. Kemperman · Pacific Journal of Mathematics · 1991
Suppose a number of X-ray pictures is taken of the same object, but from different directions.One typically likes to know to what degree the pictures determine the object and exactly when an object is uniquely determined.Replacing picture taking by projections, that is, images relative to specified mappings, these same problems are easily formulated for higher dimensions and even for abstract spaces.The objects on hand might be data structures.With this general framework, starting from an arbitrary but fixed collection of mappings, we study a new and very useful class of objects (sets) each of which is uniquely determined by its projections.In the process, we disprove a previously conjectured characterization of uniqueness relative to the one-dimensional projections in R n .For all situations where the underlying space is finite, a complete and rather simple characterization of uniqueness is obtained.