Non-Connected Convexities and Applications

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The notion of convex set, known according to its numerous applications in linear spaces due to its connectivity which leads to separation and support properties, does not imply, necessarily, the connectivity. This aspect of non-connectivity hidden under the convexity is discussed in this text. The property of non-preserving the connectivity leads to a huge extent of the domain of convexity. This book contains the classification of 100 notions of convexity, using a generalized convexity notion, which is the classifier, ordering the domain of concepts of convex sets. Also, it opens the wide range of applications of convexity in non-connected environments. Applications in pattern recognition, in discrete programming, with practical applications in pharmaco-economics are discussed. Both the synthesis part and the applied part should make the book useful for more levels of readers.