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Based on the widely shared intuition that real things that can be defined by simple systems should have simple topologies, presents theorems that estimate the complexity of the topology of geometric objects by the cumbersomeness of the defining equations, and reveals that the determining factor is not the degree of the equations, but merely the number of monomials appearing in them. The results give new information on level sets of elementary functions, and even algebraic equations. First published in Russian in 1987. Annotation c. Book News, Inc., Portland, OR (booknews.com)