<An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee (2011)> shows that this is a <tensor> that represents the <volume of a parallelepiped>.

It takes as input three vectors, and outputs one real number, the volume. And it is linear on each vector. This perfectly satisfied the definition of a tensor of <order of a tensor>[order] (3,0).

Given a basis $(e_i, e_j, e_k)$ and a function that return the volume of a parallelepiped given by three vectors $V(v_1, v_2, v_3)$, $\varepsilon_{ikj} = V(e_i, e_j, e_k)$.


Discussion on "Levi-Civita symbol as a tensor" by Ciro Santilli 32