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.
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