Geodesic
On the sets A + A and A - A
Acta Universitatis Lodziensis. Folia Mathematica, Tome 05 (1992)

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In the paper, an example of a closed set F of real numbers satisfying the conditions F + F = [0, 2] and F - F ≠ [-1, 1] is presented. It is a negative answer to the problem posed by M. Laczkovich. Also, some necessary condition for sets of this type is formulated. 
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     author = {Jasku{\l}a, Janusz and Lech, Jaros{\l}aw},
     title = {On the sets {A} + {A} and {A} - {A}},
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Jaskuła, Janusz; Lech, Jarosław. On the sets A + A and A - A. Acta Universitatis Lodziensis. Folia Mathematica, Tome 05 (1992). http://geodesic.mathdoc.fr/item/AULFM_1992_05_a12/