On Computer Topological Function Space

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.

Regular Covering Space in Digital Covering Theory and Its Applications

“…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.…”

Category Which Is Suitable for Studying Khalimsky Topological Spaces With Digital Connectivity

“…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].…”

“…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.…”

“…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].…”

Comparison of Continuities in Digital Topology

“…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].…”