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for all a, b ∈ E and 0 ≤ t ≤ 1. Equivalently, f is affine if the map T :E → F , defined by Tx = fx− f(0), is linear. An isometry need not be affine. To see this, let E be the real line R, let F be(More)
The upper set à of a metric space A is a subset of A × (0,∞) , consisting of all pairs (x, |x − y|) with x, y ∈ A , x = y . We consider various properties of à and a metric of à , called the broken(More)
1.1. Notation. Throughout this article, E and F are real Banach spaces (sometimes Hilbert spaces or just euclidean spaces) of dimension at least one. The norm of a vector x is written as |x|. In a(More)