Fixed Point Sets of k -Continuous Self-Maps of m -Iterated Digital Wedges

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 9, 1-26

Abstract: Let C k n , l be a simple closed k -curves with l elements in Z n and W : = C k n , l ∨ ? ∨ C k n , l ? m - times be an m -iterated digital wedges of C k n , l , and F ( C o n k ( W ) ) be an alignment of fixed point sets of W . Then, the aim of the paper is devoted to investigating various properties of F ( C o n k ( W ) ) . Furthermore, when proceeding with this work, this paper addresses several unsolved problems. To be specific, we firstly formulate an alignment of fixed point sets of C k n , l , denoted by F ( C o n k ( C k n , l ) ) , where l ( ≥ 7 ) is an odd natural number and k ≠ 2 n . Secondly, given a digital image ( X , k ) with X ? = n , we find a certain condition that supports n − 1 , n − 2 ∈ F ( C o n k ( X ) ) . Thirdly, after finding some features of F ( C o n k ( W ) ) , we develop a method of making F ( C o n k ( W ) ) perfect according to the (even or odd) number l of C k n , l . Finally, we prove that the perfectness of F ( C o n k ( W ) ) is equivalent to that of F ( C o n k ( C k n , l ) ) . This can play an important role in studying fixed point theory and digital curve theory. This paper only deals with k -connected digital images ( X , k ) such that X ? ≥ 2 .

Keywords: digital wedge; alignment; perfect; k-contractibility; digital k-curve; fixed point set; digital image; digital topology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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