Existence of the Category DTC₂(K) Equivalent to the Given Category KAC₂

For a given category KAC₂, the present paper deals with an existence problem of the category DTC₂(k) which is equivalent to KAC₂, where DTC₂(k) is the category whose objects are simple closed k-curves with even number l of elements in Zⁿ, l ≠ 6 and morphisms are (digitally) k-continuous maps, and...

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Збережено в:
Бібліографічні деталі
Дата:2015
Автор: Han, S.-E.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2015
Назва видання:Український математичний журнал
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Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/166474
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Existence of the Category DTC₂(K) Equivalent to the Given Category KAC₂ / S.-E. Han // Український математичний журнал. — 2015. — Т. 67, № 8. — С. 1122–1133. — Бібліогр.: 10 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Резюме:For a given category KAC₂, the present paper deals with an existence problem of the category DTC₂(k) which is equivalent to KAC₂, where DTC₂(k) is the category whose objects are simple closed k-curves with even number l of elements in Zⁿ, l ≠ 6 and morphisms are (digitally) k-continuous maps, and KAC₂ is the category whose objects are simple closed A-curves and morphisms are A-maps. To address this issue, the paper starts with the category, denoted by KAC₁, whose objects are connected nD Khalimsky topological subspaces with Khalimsky adjacency and morphisms are A-maps in [Han S. E., Sostak A. A compression of digital images derived from a Khalimsky topological structure // Comput. and Appl. Math. – 2013. – 32. – P. 521 – 536]. Based on this approach, in KAC₁ the paper proposes the notions of an A-homotopy and an A-homotopy equivalence, and classifies spaces in KAC₁ or KAC₂ in terms of an A-homotopy equivalence. Finally, the paper proves that for a given category KAC₂ there is DTC₂(k) which is equivalent to KAC₂.