Abstract
Let X be a topological vector space of complex-valued sequences and Y be a subset of X. We provide conditions for (X∖Y)∪{0} to contain uncountably infinitely many linearly independent dense vector subspaces of X. We also provide conditions for (X∖Y)∪{0} to contain uncountably infinitely many linearly independent closed infinite-dimensional vector subspaces of X. We apply these results to a chain of spaces containing the ℓp spaces.
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