Generalized Normal Product Adjacency in Digital Topology

TL;DR

This paper explores the properties of Cartesian products of digital images using normal product adjacency, revealing new product properties that differ from those using traditional $c_u$-adjacencies.

Contribution

It introduces the use of normal product adjacency in digital topology to establish new product properties for digital images.

Findings

Normal product adjacency enables new product properties.

Differences between normal product and $c_u$-adjacencies are highlighted.

Some properties valid under normal product adjacency are unknown or invalid with $c_u$-adjacencies.

Abstract

We study properties of Cartesian products of digital images for which adjacencies based on the normal product adjacency are used. We show that the use of such adjacencies lets us obtain many "product properties" for which the analogous statement is either unknown or invalid if, instead, we were to use $c_u$-adjacencies.