Abstract
The linear character of functional analysis underscores the entire subject. In addition to geometric structures such as subspaces, it can be important to consider subsets C of vector spaces V that are locally linear in the sense that C contains the line segment in V between every pair of points of C. That is, if u, v ∈ C, then so is tu + (1 − t)v for every t ∈ [0, 1]. Such sets are said to be convex and they are crucial structures in functional analysis, useful for both the geometrical and topological information that they reveal about a space V.
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© 2016 Springer International Publishing Switzerland
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Farenick, D. (2016). Convexity. In: Fundamentals of Functional Analysis. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-45633-1_7
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DOI: https://doi.org/10.1007/978-3-319-45633-1_7
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-45633-1
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