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

An Application of the supremum cosine angle between multiplication invariant spaces in $L^2(X; \mc H)$