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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2006, Number 2, Pages 29–34
(Mi basm93)
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This article is cited in 2 scientific papers (total in 2 papers)
On the Division of Abstract Manifolds in Cubes
Mariana Bujac, Sergiu Cataranciuc, Petru Soltan Moldova State University, Faculty of Mathematics and Computer Science, Chişinău, Moldova
Abstract:
We prove that in the class of abstract multidimensional manifolds without borders only torus $V_1^n$ of dimension $n\ge 1$ can be divided in abstract cubes with the property: every face $I^m$ from $V_1^n$ is shared by $2^{n-m}$ cubes, $m=0,1,\ldots,n-1$. The abstract torus $V_1^n$ is realized in $E^d$, $n+1\le d\le 2n+1$, so it results that in the class of all $n$-dimensional combinatorial manifolds [1] only torus respects this propriety. Torus is autodual because of this propriety.
Keywords and phrases:
Abstract manifold, abstract cubic manifold, cubiliaj, Euler characteristic.
Citation:
Mariana Bujac, Sergiu Cataranciuc, Petru Soltan, “On the Division of Abstract Manifolds in Cubes”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2006, no. 2, 29–34
Linking options:
https://www.mathnet.ru/eng/basm93 https://www.mathnet.ru/eng/basm/y2006/i2/p29
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Abstract page: | 446 | Full-text PDF : | 68 | References: | 59 | First page: | 1 |
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