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Sur les coupures de l'espace

Stefan MazurkiewiczStefan Straszewicz — 1927

Fundamenta Mathematicae

Le but de cette note est de démontrer deux théorèmes sur les coupures de R^3. Théorème: Si A_1, A_2 sont des ensembles fermes, dont aucun ne coupe entre les points a, b et si A_1A_2 n'est pas entrelaçable, alors A_1+A_2 ne coupe pas R^3 entre a et b. Théorème: A_1, A_2 étant deux ensembles fermes dont aucun ne coupe R^3, leur somme A_1+A_2 coupe R^3, si A_1A_2 est entrelaçable sans que A_1 et A_2 le soient.

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