Abstract
The main goal of this paper is to prove a Digital Jordan- Brouwer Theorem and an Index Theorem for simplicity 26-surfaces. For this, we follow the approach to Digital Topology introduced in [2], and find a digital space such that the continuous analogue of each simplicity 26-surface is a combinatorial 2-manifold. Thus, the separation theorems quoted above turn out to be an immediate consequence of the general results obtained in [2] and [3] for arbitrary digital n-manifolds.
This work has been partially supported by the project DGES TIC2000-1368-C03-01.
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Ciria, J.C., Domínguez, E., Francés, A.R. (2002). Separation Theorems for Simplicity 26-Surfaces. In: Braquelaire, A., Lachaud, JO., Vialard, A. (eds) Discrete Geometry for Computer Imagery. DGCI 2002. Lecture Notes in Computer Science, vol 2301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45986-3_4
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DOI: https://doi.org/10.1007/3-540-45986-3_4
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