论文标题
在hurewicz定理的平均维度的类似
On an analogue of the Hurewicz theorem for mean dimension
论文作者
论文摘要
Hurewicz定理是经典维度理论的基本结果，该理论涉及降低拓扑维度的连续图。我们研究其模拟是否适合动态系统的平均维度。我们的第一个主要结果表明，Hurewicz定理的类似物总体上不适合平均维度。我们的第二个主要结果表明，如果基本系统的平均维度为零，则它是正确的。
The Hurewicz theorem is a fundamental result in classical dimension theory concerning continuous maps which lower topological dimension. We study whether or not its analogue holds for mean dimension of dynamical systems. Our first main result shows that an analogue of the Hurewicz theorem does not hold for mean dimension in general. Our second main result shows that it holds true if a base system has zero mean dimension.
