The Jordan-Brouwer theorem for the digital normal n-space Zn
Alexander V. Evako
TL;DR
This paper explores properties of digital spaces modeled as graphs, establishing conditions for digital manifolds and spheres, and proves a digital version of the Jordan-Brouwer theorem for the normal digital n-space Zn.
Contribution
It introduces conditions for digital n-manifolds and spheres and proves a digital Jordan-Brouwer theorem for the normal digital n-space Zn.
Findings
Conditions for digital n-manifolds and spheres identified
Digital Jordan-Brouwer theorem proved for Zn
Properties of partitions of digital spaces studied
Abstract
In this paper we investigate properties of digital spaces which are represented by graphs. We find conditions for digital spaces to be digital n-manifolds and n-spheres. We study properties of partitions of digital spaces and prove a digital analog of the Jordan-Brouwer theorem for the normal digital n-space Zn.
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Taxonomy
TopicsDigital Image Processing Techniques · Interconnection Networks and Systems