论文标题
同态关系在某些类别的紧凑型与有限拓扑维度上的复杂性
The complexity of homeomorphism relations on some classes of compacta with bounded topological dimension
论文作者
论文摘要
从不变的描述集理论的角度来看，我们正在处理同态等效性关系对某些类别的Metrizable Compacta的复杂性。我们证明，在平面中绝对缩回的同态等效性关系是可依层的borel borel，与可数图的同构等效关系有关。为了强调这一结果的清晰度，我们证明，平面中局部连接的连续图的同态关系，也不是绝对缩回的同态性关系在$ \ mathbb r^3 $中均无法与可计数图的同构相关性降低。我们还通过构建$ \ Mathbb r^n $紧凑型子集的同质形态等效性关系以及正同态同态等效性关系$ [0,1]^n $与同源$ -N $ -DIMENSINEM的紧凑型子集的紧凑性关系相关性，并从同质性的同态等效关系中构建了Chang and Gao的最新结果。 r^{n+1} $。
We are dealing with the complexity of the homeomorphism equivalence relation on some classes of metrizable compacta from the viewpoint of invariant descriptive set theory. We prove that the homeomorphism equivalence relation of absolute retracts in the plane is Borel bireducible with the isomorphism equivalence relation of countable graphs. In order to stress the sharpness of this result, we prove that neither the homeomorphism relation of locally connected continua in the plane nor the homeomorphism relation of absolute retracts in $\mathbb R^3$ is Borel reducible to the isomorphism relation of countable graphs. We also improve the recent results of Chang and Gao by constructing a Borel reduction from both the homeomorphism equivalence relation of compact subsets of $\mathbb R^n$ and the ambient homeomorphism equivalence relation of compact subsets of $[0,1]^n$ to the homeomorphism equivalence relation of $n$-dimensional continua in $\mathbb R^{n+1}$.
