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 K1 x .... x 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) x ... x K(n+1)). Other properties of product of Peano curves without free arcs are also proved. (C) 2010 Elsevier B.V. All rights reserved.