The number of isomorphism classes of spreads (Q1263081)

A generalized chord of the closed unit disk \(D\) (in the complex plane) is an arc \([x,y]\) of \(D\), such that \(x\neq y\) and \([x,y]\cap \partial D=\{x,y\}\). Similarly a spread is a continuous function \(s\) which assigns to each \(x\in \partial D\) a generalized chord of \(D\), with the following properties for all \(x,y\in \partial D:\) \(y\in s(x)\Rightarrow s(y)=s(x)\); \(y\not\in s(x) \Rightarrow s(y)\cap s(x)\) consist of one point (in \(D\setminus \partial D).\) The author shows that there are c (the cardinality of the continuum) many pairwise nonisomorphic spreads, and he shows how to make these spreads pairwise finitarily isomorphic. In this way, he proves conjectures of \textit{B. Grünbaum} [``Arrangements and spreads'' (1972; Zbl 0249.50011)].