Defects of Properties in Mathematics: Quantitative Characterizations

Defects of Properties in Mathematics: Quantitative Characterizations

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This book introduces a method of research which can be used in various fields of mathematics. It examines, in a systematic way, the quantitative characterizations of the ¿deviation from a (given) property¿, called the ¿defect of a property¿, in: set theory; topology; measure theory; real, complex and functional analysis; algebra; geometry; number theory; fuzzy mathematics.Besides well-known ¿defects¿, the book introduces and studies new ones, such as: measures of noncompactness for fuzzy sets; fuzzy and intuitionistic entropies; the defect of (sub, super)additivity; complementarity; mono...