标题： 风扇、phan（支持者）和平底锅 显示英文标题

标题： Fans, phans and pans

摘要： 一个扇形是一个弧连通的连续统，它具有遗传单连通性并且恰好有一个分枝点。 许多已知的扇形例子被构造为1维连续统，这些连续统是由一些仅在一点相交的弧组成的。 1954年，博苏克证明了每个扇形都是由一些仅在一点相交的弧组成的1维连续统。 但目前尚不清楚这个性质是否等价于成为扇形。 在本文中，我们证明了，在两个附加假设下，所有这样的弧的并集都是一个扇形。 显示英文摘要

摘要： A fan is an arcwise-connected continuum, which is hereditarily unicoherent and has exactly one ramification point. Many of the known examples of fans were constructed as 1-dimensional continua that are unions of arcs which intersect in exactly one point. Borsuk proved in 1954 that each fan is a 1-dimensional continuum which is the union of arcs intersecting in exactly one point. But it is not yet known if this property is equivalent to being a fan. In this paper, we show that under two additional assumptions, every such union of arcs is a fan.