Discrete versions of the Beckman - Quarles theorem from the definability results of Raphael M . Robinson
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چکیده
We derive author's discrete forms of the Beckman-Quarles theorem from the definability results of Raphael M. Robinson. The classical Beckman-Quarles theorem states that each map from R n to R n (n > 1) preserving all unit distances is an isometry, see [1]-[3]. In this note we derive author's discrete forms of this theorem ([6]) from the definability results of Raphael M. Robinson (see [4] and also [5]). The following two theorems of Raphael M. Robinson are formulated in [4] in a more general form. Theorem 1a. Let n > 1 be a fixed integer number. All algebraic distances in R n can be defined existentially in terms of the unit distance
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2 00 1 Discrete versions of the Beckman - Quarles theorem from the definability results of Raphael M .
We derive author's discrete forms of the Beckman-Quarles theorem from the definability results of Raphael M. Robinson. The classical Beckman-Quarles theorem states that each map from R n to R n (n > 1) preserving all unit distances is an isometry, see [1]-[3]. In this note we derive author's discrete forms of this theorem ([6]) from the definability results of Raphael M. Robinson (see [4] and a...
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