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...
Збережено в:
Дата: | 2015 |
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Автор: | |
Формат: | Стаття |
Мова: | English |
Опубліковано: |
Інститут математики НАН України
2015
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Назва видання: | Український математичний журнал |
Теми: | |
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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of UkraineРезюме: | 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. |
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