Fixed Point Sets of Digital Curves and Digital Surfaces

Sang-Eon Han
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Sang-Eon Han: Department of Mathematics Education, Institute of Pure and Applied Mathematics, Jeonbuk National University, Jeonju-City Jeonbuk 54896, Korea

Mathematics, 2020, vol. 8, issue 11, 1-25

Abstract: Given a digital image (or digital object) ( X , k ) , we address some unsolved problems related to the study of fixed point sets of k -continuous self-maps of ( X , k ) from the viewpoints of digital curve and digital surface theory. Consider two simple closed k -curves with l i elements in Z n , i ∈ { 1 , 2 } , l 1 ? l 2 ≥ 4 . After initially formulating an alignment of fixed point sets of a digital wedge of these curves, we prove that perfectness of it depends on the numbers l i , i ∈ { 1 , 2 } , instead of the k -adjacency. Furthermore, given digital k -surfaces, we also study an alignment of fixed point sets of digital k -surfaces and digital wedges of them. Finally, given a digital image which is not perfect, we explore a certain condition that makes it perfect. In this paper, each digital image ( X , k ) is assumed to be k -connected and X ? ≥ 2 unless stated otherwise.

Keywords: digital wedge; alignment; perfect; fixed point set; digital k-surface; digital topology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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