论文标题
在粘性几乎零维空间上
On cohesive almost zero-dimensional spaces
论文作者
论文摘要
我们在几乎零维空间中调查了C型组，表明关闭的$σ$ c-set是c-set。作为推论，我们证明，每个边缘$σ$ compact几乎零维空间都是零维空间，并且每个凝聚力几乎零维空间无处都是合理的。为了显示这些结果很清晰，我们构建了带有爆炸点的连接的边缘 - 污点。我们还显示了$（$ cantor set $）$$ \ times \ times \ mathbb r $的每个凝聚力几乎为零的子空间。
We investigate C-sets in almost zero-dimensional spaces, showing that closed $σ$C-sets are C-sets. As corollaries, we prove that every rim-$σ$-compact almost zero-dimensional space is zero-dimensional and that each cohesive almost zero-dimensional space is nowhere rational. To show these results are sharp, we construct a rim-discrete connected set with an explosion point. We also show every cohesive almost zero-dimensional subspace of $($Cantor set$)$$\times\mathbb R$ is nowhere dense.
