ON THE DIVISION OF ABSTRACT MANIFOLDS IN CUBES
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Institutul de Matematică şi Informatică al AŞM
Abstract
We prove that in the class of abstract multidimensional manifolds withoutborders only torusVn1of dimensionn≥1 can be divided in abstract cubes with theproperty: every faceImfromVn1is shared by 2n−mcubes,m= 0,1, . . . , n−1. Theabstract torusVn1is realized inEd, n+1≤d≤2n+1, so it results that in the class ofalln-dimensional combinatorial manifolds [1]onlytorus respects this propriety. Torusis autodual because of this propriety.
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BUJAC, Mariana, CATARANCIUC, Sergiu, SOLTAN, Petru. On the Division of Abstract Manifolds in Cubes. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2006, nr. 2(51), pp. 29-34. ISSN 1024-7696.