Some results of Morse functions in digital images
Karaca Ismet, Vergili Tane, Temizel Gokhan, Hatice Sevde Denizalti · Malaya Journal of Matematik · 2020
In many years authors have adapted some notions of topology and combinatorial topology to the digital topology. In this paper we apply some definition of discrete Morse theory to the digital topology. We define a new definition of adjacency relation to show that digital subcomplexes are digitally homotopy equivalent. We conclude that if there is no digitally critical simplex in the digital interval \([m, n]_{\mathbb{Z}}\), then the digital subcomplexes \(K(m)\) and \(K(n)\) are digitally homotopy equivalent.