The Almost Pasting Property of Digital Continuity

Abstract

The pasting property plays a significant role in studying a continuous map in general topology. Unlike the pasting property, digital continuity has some intrinsic features. In this paper we prove that digital continuity has the almost pasting property instead of the pasting one. Furthermore, as a digital version of the straightness of a metric space, we introduce the notion of k-straightness of a digital space (X, k) and study its properties which can be used in image synthesis and digital image weaving.

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

“…The current presentation of the digital continuity has been often used in digital k-curve and digital k-surface theory. Unlike the pasting property of classical continuity in topology, the digital (k 0 , k 1 )-continuity of Definition 3 has some intrinsic features [13]: Digital (k 0 , k 1 )-continuity has the almost pasting property instead of the pasting property of classical topology.…”

KD-(k0, k1)-HOMOTOPY EQUIVALENCE AND ITS APPLICATIONS

“…Unlike the pasting property of classical continuity in topology, (k 0 , k 1 )-continuity has some intrinsic features: (k 0 , k 1 )-continuity has the almost pasting property [29] instead of the pasting property of classical continuity.…”

Regular Covering Space in Digital Covering Theory and Its Applications

“…Unlike the pasting property of classical continuity in topology, (k 0 , k 1 )-continuity has some intrinsic features [27]: Digital (k 0 , k 1 )-continuity has the almost pasting property instead of the pasting property of classical topology.…”