A minimal family of open intervals generating the Borel sets (Q1174605)

A family \(\mathcal E\) of open intervals is constructed which generates the Borel structure on \(\mathbb{R}\) and is minimal in the sense that each proper subfamily of \(\mathcal E\) fails to separate some pair of points in \(\mathbb{R}\). This corrects an error in Diss. Math. 190 (1981; Zbl 0472.28002) by \textit{K. P. S. Bhaskara Rao} and \textit{B. V. Rao}. \textit{K. P. S. Bhaskara Rao} and \textit{R. M. Shortt} discovered a similar example independently. Their paper in Real Anal. Exch. 16, No. 1, 177-186 (1991; preceding review) also shows that each family of open intervals has a countable subfamily which separates the same pairs of points as the original family.