Universal space in the Cartesian product of Peano curves without free arcs

We prove that there is the universal space for the class of n-dimensional separable metric spaces in the Cartesian product K 1 × ⋯ × K n + 1 of Peano curves without free arcs. It is also shown that the set of embeddings of any n-dimensional separable metric space X into this universal space is a residual set in C ( X , K 1 × ⋯ × K n + 1 ) . Other properties of product of Peano curves without free arcs are also proved.