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- W2963390532 abstract "Abstract In this article, a notion of Schauder equivalence relation ℝ ℕ / L is introduced, where L is a linear subspace of ℝ ℕ and the unit vectors form a Schauder basis of L . The main theorem is to show that the following conditions are equivalent: (1) the unit vector basis is boundedly complete; (2) L is a F σ in ℝ ℕ ; (3) ℝ ℕ / L is Borel reducible to ℓ ∞ . We show that any Schauder equivalence relation generalized by a basis of ℓ 2 is Borel bireducible to ℝ ℕ / ℓ 2 itself, but it is not true for bases of c 0 or ℓ 1 . Furthermore, among all Schauder equivalence relations generated by sequences in c 0 , we find the minimum and the maximum elements with respect to Borel reducibility." @default.
- W2963390532 created "2019-07-30" @default.
- W2963390532 creator A5057617556 @default.
- W2963390532 date "2017-12-01" @default.
- W2963390532 modified "2023-10-17" @default.
- W2963390532 title "ON EQUIVALENCE RELATIONS GENERATED BY SCHAUDER BASES" @default.
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- W2963390532 doi "https://doi.org/10.1017/jsl.2017.67" @default.
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