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Digital
n
-Pseudomanifold and n-Weakmanifold in a Binary (
n
+ 1)-Digital Image
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Digital n-Pseudomanifold and n-Weakmanifold in a Binary ( n + 1)-Digital Image
Mohammed Khachan7  , Patrick Chenin8 and Hafsa Deddi9
| (7) |
Department of Computer Science (IRCOM-SIC), University of Poitiers, Bd 3, Teleport 2, Bp 179, 86960 Futuroscope cedex, France |
| (8) |
LMC-IMAG, University Joseph Fourier, 51 Rue des Mathematiques, BP 53, 38420 Grenoble cedex 9, France |
| (9) |
LACIM, University of Quebec at Montreal, C.P 8888, Succ. Centre-ville, H3C 3P8 Montreal, Quebec, Canada |
Abstract
We introduce the notion of digital n-pseudomanifold and digital n-weakmanifold in (n+1)-digital image, in the context of (2n, 3
n
-1)- adjacency, and prove the digital version of the Jordan-Brouwer separation theorem for those classes. To accomplish this
objective, we construct a polyhedral representation of the n-digital image, based on cubical complex decomposition. This enables
us to translate some results from polyhedral topology into the digital space. Our main result extends the class of “thin”
objects that are defined locally and verifies the Jordan-Brouwer separation theorem.
Keywords digital topology - combinatorial topology - discrete spaces - combinatorial manifolds
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