Abstract
The main purpose of the paper is to show that, for each real normed space Y of infinite dimension, each number L > 0, and each at most countable set Q ⊂ ℝ, there exists a Lipschitz mapping ƒ: ℝ → Y, with constant L, whose graph has a tangent everywhere, whereas ƒ is not differentiable at any point of Q.
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