Connected sum of digital closed surfaces

Banach fixed point theorem from the viewpoint of digital topology

“…In Definition 2.2, in case n 0 = n 1 and k 0 = k 1 := k, we call it a k-isomorphism [8,9]. In addition, we denote by X ≈ k Y a k-isomorphism from X to Y .…”

“…In relation to the study of a Banach contraction principle of a closed 18-surface [6], we need to recall basic notions from digital k-surface theory [2,3,9,10,21,22]. In a digital image (X, k), a point x ∈ X is called a k-corner if x is k-adjacent to two and only two points y, z ∈ X such that y and z are k-adjacent to each other [3].…”

“…To work these out in details, Ege et al [6] used the notion of a digital metric space, a digital version of the Banach contraction principle and some properties from digital topology [2,3,8,9,10,20,21,22,26]. However, since the paper [6] has many things to be refined and corrected, the present paper makes these approaches from (1) to (4) above improved.…”

Computing Higher Dimensional Digital Homotopy Groups

“…between f and g is called a digital homotopy relative to A between f and g if for all a ∈ A, and for all t [11]). Then we say that f and [2] between f and g.…”

Simplicial Relative Cohomology Rings of Digital Images

“…Many researchers (Rosenfeld [24], Kopperman [20], Kong [19], Malgouyres [21], Boxer [4,5,6,7,9], Han [11,12], Karaca [1,10]) have contributed to digital topology with their studies. They wish to characterize the properties of digital images with tools from Algebraic Topology.…”