Alexandroff pretopologies for structuring the digital plane
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F17%3APU119234" target="_blank" >RIV/00216305:26210/17:PU119234 - isvavai.cz</a>
Result on the web
<a href="https://ac.els-cdn.com/S0166218X16302670/1-s2.0-S0166218X16302670-main.pdf?_tid=b5db0aee-e1e1-11e7-b51a-00000aab0f02&acdnat=1513374708_82e3d74b75420ea8adca800b18dc4e43" target="_blank" >https://ac.els-cdn.com/S0166218X16302670/1-s2.0-S0166218X16302670-main.pdf?_tid=b5db0aee-e1e1-11e7-b51a-00000aab0f02&acdnat=1513374708_82e3d74b75420ea8adca800b18dc4e43</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.dam.2016.06.002" target="_blank" >10.1016/j.dam.2016.06.002</a>
Alternative languages
Result language
angličtina
Original language name
Alexandroff pretopologies for structuring the digital plane
Original language description
We explore the possibility of employing Alexandroff pretopologies as structures on the digital plane Z^2 convenient for the study of geometric and topological properties of digital images. These pretopologies are known to be in one-to-one correspondence with reflexive binary relations so that graph-theoretic methods may be used when investigating them. We discuss such Alexandroff pretopologies on Z2 that possess a rich variety of digital Jordan curves obtained as circuits in a natural graph with the vertex set Z2. Of these pretopologies, we focus on the minimal ones and study their quotient pretopologies on Z2 which are shown to allow for various digital Jordan curve theorems. We also develop a method for identifying Jordan curves in the minimal pretopological spaces by using Jordan curves in one of their quotient spaces. Using this method, we conclude the paper with proving a digital Jordan curve theorem for the minimal pretopologies.
Czech name
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Czech description
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Classification
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
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/LO1202" target="_blank" >LO1202: NETME CENTRE PLUS</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete Applied Mathematics
ISSN
0166-218X
e-ISSN
1872-6771
Volume of the periodical
216
Issue of the periodical within the volume
2
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
12
Pages from-to
323-334
UT code for WoS article
000390504100002
EID of the result in the Scopus database
2-s2.0-84977618285