Digital Hopf Spaces and Their Duals

Dae-Woong Lee and Akbar Ali

Journal of Mathematics, 2022, vol. 2022, 1-13

Abstract: In this article, we study the fundamental notions of digital Hopf and co-Hopf spaces based on pointed digital images. We show that a digital Hopf space, a digital associative Hopf space, a digital Hopf group, and a digital commutative Hopf space are unique up to digital homotopy type; that is, there is only one possible digital Hopf structure up to digital homotopy type on the underlying digital image. We also establish an equivalent condition for a digital image to be a digital Hopf space and investigate the difference between ordinary topological co-Hopf spaces and their digital counterparts by showing that any digital co-Hopf space is a digitally contractible space focusing on deep-learning methods in imaging science.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8435007

DOI: 10.1155/2022/8435007

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