标题： 关于栅栏和扇形的局部性质 显示英文标题

标题： On a local property of fences and fans

摘要： 两个密切相关的拓扑空间类是栅栏和风扇。 一个栅栏是一个紧致度量空间，其连通分支要么是弧要么是单点集。 一个风扇是由在公共顶点处连接弧形成的连续统，使得子连续统的交总是连通的。 我们证明每个栅栏都可以嵌入平面，并且栅栏和风扇都具有由穿孔开集组成的基。 这解决了Iztok Banič、Goran Erceg、Ivan Jelić、Judy Kennedy和Van Nall提出的问题。 显示英文摘要

摘要： Two closely related classes of topological spaces are fences and fans. A fence is a compact metric space whose components are either arcs or singletons. A fan is a continuum formed by joining arcs at a common vertex, in such a way that intersections of subcontinua are always connected. We prove that every fence can be embedded in the plane and that both fences and fans admit a basis consisting of pierced open sets. This resolves a question by Iztok Bani\v{c}, Goran Erceg, Ivan Jeli\'c, Judy Kennedy, and Van Nall.