Remarks on the Preservation of the Almost Fixed Point Property Involving Several Types of Digitizations

Abstract

This paper explores a certain relationship between the almost fixed point property (AFPP for short) of a compact and n-dimensional Euclidean space and that of its digitized space. Based on several types of digitizations, we prove that the AFPP of a compact and n-dimensional Euclidean cube is preserved by each of the U ( k ) , the L ( k ) and the Khalimsky digitizations, k ∈ 3 n − 1 , n ∈ N .

Keywords

• digital space
• <i>u</i>- and <i>l</i>-digitization
• fixed point property
• almost fixed point property
• khalimsky topology
• digital topology