An MA-digitization of Hausdorff spaces by using a connectedness graph of the Marcus-Wyse topology

作者：Han, Sang-Eon^*; Yao, Wei

来源：Discrete Applied Mathematics, 2017, 216: 335-347.

DOI：10.1016/j.dam.2016.01.007

• Digital topology
• MA-digitization
• Marcus-Wyse topology
• Marcus-Wyse adjacency
• MA-map
• M-topological graph
• M-localized neighborhood
• M-connectedness preserving map
• LMA-homeomorphism
• MA-fundamental group

The study of 2D digital spaces plays an important role in both topology and digital geometry. To propose a certain method of digitizing subspaces of the 2D Euclidean space (or Hausdorff space, denoted by R-2), the present paper follows a Marcus-Wyse (M-, for short) topological approach because the M-topology was developed for studying digital spaces in Z(2), where Z(2) is the set of points in R-2 with integer coordinates. Hence the present paper uses several tools associated with M-topology, e.g. an M-localized neighborhood of a point p is an element of Z(2), a topological graph (or a connectedness graph) induced by the M-topology (or M connectedness graph), a new type of lattice-based connectedness graph homomorphism (or lattice-based M-adjacency map, LMA-map for brevity) which are substantially helpful to MA-digitize subspaces of R-2, where "MA" means the M-adjacency (see Definition 10 and Theorem 3.9 of the present paper). Besides, the paper proposes an algorithm supporting an MA-digitization of subspaces of R-2. Furthermore, to investigate a relation between subspaces of R-2 and their corresponding MA-digitized spaces, and to classify subspaces of R-2 associated with the M-topology, the paper uses both the first homotopy group (or the fundamental group) in algebraic topology and an MA-fundamental group.

• 出版日期2017-1-10
• 单位河北科技大学