Titlebook: Convex Analysis and Beyond; Volume I: Basic Theo Boris S. Mordukhovich,Nguyen Mau Nam Textbook 2022 Springer Nature Switzerland AG 2022 Top

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https://doi.org/10.1057/9781137349927This chapter collects fundamental notions and results in vector spaces, topological spaces, topological vector spaces, and their specifications that are widely used in the subsequent chapters of the book to build the basic theory of convexity and its applications.

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BASIC THEORY OF CONVEXITY,of convex functions. Further topics on convexity, including duality and generalized differentiation theories, are considered in the subsequent chapters. Unless otherwise stated, we consider . in this chapter and the subsequent ones.

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MISCELLANEOUS TOPICS ON CONVEXITY,ion; on the study of asymptotic behavior of convex sets and functions at infinity; on the considerations of the remarkable classes of signed distance and minimal time functions; and on classical finite-dimensional results related to the Carathéodory and Helly theorems, Farkas lemma, etc.