On explicit constructions of auerbach bases in separable Banach spaces

This paper considers explicit constructions of Auerbach bases in separable Banach spaces. Answering the question of A. Pełczy{ń}ski, we prove by construction the existence of Auerbach basis in arbitrary subspace of $c_0$ of finite codimension and in the space $C(K)$ for $K$ compact countable metric space.

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