Distributivity of a segmentation lattice

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F23%3APU149979" target="_blank" >RIV/00216305:26210/23:PU149979 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.dam.2023.06.028" target="_blank" >https://doi.org/10.1016/j.dam.2023.06.028</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.dam.2023.06.028" target="_blank" >10.1016/j.dam.2023.06.028</a>

Result language
angličtina
Original language name
Distributivity of a segmentation lattice
Original language description
Closure spaces, namely the finite ones, with closed singletons are studied on the level of segmentations - partitions of the space into closed subsets. Segmentations form a lattice and we study spaces for which this lattice is distributive. Studying these spaces may help understanding mathematical background for segmentation of a digital image. A crucial notion is that of connectively irreducible sets which can be defined in any finite closure space. The paper provides several equivalent conditions for segmentational distributivity in terms of triples of closed sets, connected systems of closed sets, property of induced closure operator on down-sets of connectively irreducible sets, and finally by restriction (or disability) of existence of certain sublattices.& COPY; 2023 Elsevier B.V. All rights reserved.
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
10100 - Mathematics

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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