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This paper investigates the closed subsets of the vector space of multi-indexed sequences over a field with respect to the pointwise convergence topology. These closed subsets are shown to be the orthogonal complements of the subspaces of sequences with finite support in the vector space. The notion of orthogonality is established using a natural scalar product on these vector spaces.
Andriamifidisoa et al. (Thu,) studied this question.
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