Hairy point

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The hairy point is a continuum that is the union of an infinite sequence of arcs $a_1,a_2,\ldots$ such that all the arcs start at a point $v$, given any $i,j$ $a_i \cap a_j = \{v\}$, and $\displaystyle\lim_{k \rightarrow \infty} \mathrm{diam}(a_k)=0$. Sometimes the arcs $a_i$ are called "hairs" and the vertex $v$ is called the "follicle".

Hairy point.png