A 3D digital Jordan-Brouwer separation theorem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26230%2F20%3APU138922" target="_blank" >RIV/00216305:26230/20:PU138922 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/content/pdf/10.1007%2Fs40314-020-01249-w.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007%2Fs40314-020-01249-w.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s40314-020-01249-w" target="_blank" >10.1007/s40314-020-01249-w</a>

Result language
angličtina
Original language name
A 3D digital Jordan-Brouwer separation theorem
Original language description
We introduce and discuss a concept of connectedness induced by an n-ary relation (n>1 an integer). In particular, for every integer n>1, we define an n-ary relation R on the digital line Z and equip the digital space with the n-ary relation S obtained as a special product of three copies of R. For n=2, the connectedness induced by S coincides with the connectedness given by the Khalimsky topology on the 3D digital space and we show that, for every integer n>2, it allows for a digital analog of the Jordan-Brouwer separation theorem for three-dimensional spaces. An advantage of the connectedness induced by S over that given by the Khalimsky topology is shown, too.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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