Generalized digital $(k_0, k_1)$-homeomorphism

Abstract

The aim of this paper is to introduce a generalized digital $(k_0, k_1)$-homeomorphism of the digital curve and the digital surface in $\mathbb{Z}^n$.  The generalized digital $(k_0, k_1)$-continuity is studied with the $n$ kinds of $k$-adjacency relations in $\mathbb{Z}^n$.  The $k$-type digital fundamental group of the digital image comes from the generalized digital $(k_0, k_1)$-homotopy, $i \in \{0, 1\}$.  Furthermore, we show how a digital $(k_0, k_1)$-homeomophism induces a digital fundamental group $(k_0, k_1)$-isomorphism.