Digital $k$-continuity, digital $k$-isomorphism, local $k$-isomorphism, radius $2$-local $k$-isomorphism, and digital $k$-homotopy

TL;DR

This paper explores various concepts of digital continuity, isomorphism, and homotopy in digital topology, clarifying previous inaccuracies and proposing precise definitions based on Khalimsky's framework.

Contribution

It introduces corrected definitions and insights into digital $k$-continuity, isomorphism, and homotopy, addressing errors in prior literature.

Findings

Clarification of digital $k$-isomorphism concepts

Correction of inaccuracies in Boxer's work

Enhanced understanding of digital homotopy

Abstract

The present paper refers to the notions of digital continuity, digital $k$-isomorphism, local $k$-isomorphism, radius $2$-local $k$-isomorphism, and digital $k$-homotopy motivated by the Khalimsky's version. We discuss something incorrectly mentioned in Boxer's papers and suggest some accurate information.