Abstract:Abstract. In this paper, we give and study the notion of computer topological function space between computer topological spaces with k iadjacency, i ∈ {0, 1}. Using this notion, we study various properties of topologies of a computer topological function space.
“…Furthermore, by using some properties of various types of homeomorphisms and a function space in computer topology [15,24], we can study computer topological analog of the results in this paper.…”
Section: Concluding Remark and Further Workmentioning
Abstract. As a survey-type article, the paper reviews some results on a regular covering space in digital covering theory. The recent paper [10](see also [12]) established the notion of regular covering space in digital covering theory and studied its various properties. Besides, the papers [14, 16] developed a discrete Deck's transformation group of a digital covering. In this paper we study further their properties. By using these properties, we can classify digital covering spaces. Finally, the paper proposes an open problem.
“…Furthermore, by using some properties of various types of homeomorphisms and a function space in computer topology [15,24], we can study computer topological analog of the results in this paper.…”
Section: Concluding Remark and Further Workmentioning
Abstract. As a survey-type article, the paper reviews some results on a regular covering space in digital covering theory. The recent paper [10](see also [12]) established the notion of regular covering space in digital covering theory and studied its various properties. Besides, the papers [14, 16] developed a discrete Deck's transformation group of a digital covering. In this paper we study further their properties. By using these properties, we can classify digital covering spaces. Finally, the paper proposes an open problem.
“…Motivated by the Alexandroff space [1], the Khalimsky nD space (briefly, (Z n , T n )) was established and the study of its properties includes the papers [9,12,15]. In this paper we consider a subset X ⊂ Z n as a subspace of (Z n , T n ), denoted by (X, T n X ), n ≥ 1 [5,9,10].…”
Section: Introductionmentioning
confidence: 99%
“…In relation to the study of subsets of the Euclidean nD space with integer coordinates, we have often used the Khalilmsky topological structure [5,9,10,12,15]. Let Z, N and Z n represent the sets of integers, natural numbers and points in the Euclidean n-dimensional space with integer coordinates, respectively.…”
Section: Introductionmentioning
confidence: 99%
“…However, if a map f : (X, T n 0 X ) → (Y, T n 1 Y ) performs Khalimsky continuity and digital connectivity, then it can be very useful in digital topology. Thus, we have often studied a Khalimsky topological space with digital k-connectivity of Z n , n ∈ N [9,10] (see Definition 1) and further, used a map preserving digital connectivity [5].…”
Abstract. Let X n,k be a Khalimsky topological n dimensional subspace with digital k-connectivity. In relation to the classification of spaces X n,k , by comparing several kinds of continuities and homeomorphisms, the paper proposes a category which is suitable for studying the spaces X n,k .
“…Digital topology including Khalimsky topology has been often used for studying various properties of objects in Z n [2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19].…”
Abstract. Since there are several kinds of continuities of maps between digital spaces, the paper compares them, which can play an important role in digital topology and discrete geometry.
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