  In the current study, we explore digital homology and cohomology modules, and
investigate their fundamental properties on pointed digital images. We also
examine pointed digital Hopf spaces and base point preserving digital Hopf
functions between the pointed digital Hopf spaces with suitable digital
multiplications, and explore the digital primitive homology and cohomology
classes, the digital Pontryagin algebras and coalgebras on the digital Hopf
spaces as digital images.
