In this article, we describe the supremum cosine angle between two
multiplication invariant (MI) spaces and its connection with the closedness of
the sum of those spaces. The results obtained for MI spaces are preserved by
the corresponding fiber spaces almost everywhere. Employing the Zak transform,
we obtain the results for translation invariant spaces on locally compact
groups by action of its closed abelian subgroup. Additionally, we provide the
application of our results to sampling theory