论文标题
岸点存在问题等效于非块点存在问题
The Shore Point Existence Problem is Equivalent to the Non-Block Point Existence Problem
论文作者
论文摘要
我们证明这三个命题是等效的：$（a）$每个Hausdorff Continuum有两个或更多的海岸点。 $（b）$每个Hausdorff Continuum有两个或多个非块点。 $（c）$每个Hausdorff连续体在每个点都是沿海。因此，这三个属性失败是一致的。我们还给出以下岸点的特征：Continuum $ x $的点$ p $是岸点，并且仅当$ \ {k \ in C（x）中有subcontinua的净值：k \ subsetk（p） - p \} - p \} $倾向于vietoris the vietoris the vietoris拓扑。这与仅要求净元素包含在$ x-p $中的标准表征形成对比。此外，我们证明了不可分解的连续体的每个点都是海岸点。
We prove the three propositions are equivalent: $(a)$ Every Hausdorff continuum has two or more shore points. $(b)$ Every Hausdorff continuum has two or more non-block points. $(c)$ Every Hausdorff continuum is coastal at each point. Thus it is consistent that all three properties fail. We also give the following characterisation of shore points: The point $p$ of the continuum $X$ is a shore point if and only if there is a net of subcontinua in $\{K \in C(X): K \subset κ(p) - p\}$ tending to $X$ in the Vietoris topology. This contrasts with the standard characterisation which only demands the net elements be contained in $X-p$. In addition we prove every point of an indecomposable continuum is a shore point.
