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

作者：Michalik Dana^*

来源：Topology and Its Applications, 2010, 157(7): 1228-1236.

DOI：10.1016/j.topol.2010.02.030

• Covering dimension
• Peano curve
• Embedding
• ANR

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.

• 出版日期2010-5-1