For a given category KAC 2 , the present paper deals with the existence problem for the category DTC 2 (k), which is equivalent to KAC 2 , where DTC 2 (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 KAC 2 is a category whose objects are simple closed A-curves and morphisms are A-maps. To address this issue, the paper starts from the category denoted by KAC 1 whose objects are connected nD Khalimsky topological subspaces with Khalimsky adjacency and morphisms are A-maps in [S. E. Han and A. Sostak, Comput. Appl. Math., 32, 521–536 (2013)]. Based on this approach, in KAC 1 the paper proposes the notions of A-homotopy and A-homotopy equivalence and classifies the spaces in KAC 1 or KAC 2 in terms of the A-homotopy equivalence. Finally, the paper proves that, for Sa given category KAC 2 , there is DTC 2 (k), which is equivalent to KAC 2 .
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 8, pp. 1122–1133, August, 2015.
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Han, SE. Existence of the Category DTC 2 (K) Equivalent to the Given Category KAC 2 . Ukr Math J 67, 1264–1276 (2016). https://doi.org/10.1007/s11253-016-1150-4
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DOI: https://doi.org/10.1007/s11253-016-1150-4