When $\aleph _1$ many sets are contained in a countably generated $\sigma $-field
Volume 115 / 2009
Colloquium Mathematicum 115 (2009), 41-45
MSC: Primary 28A05.
DOI: 10.4064/cm115-1-5
Abstract
We discuss the problem when $\aleph _1$ sets are contained in a $\sigma $-generated $\sigma $-field on some set $X$. This is related to a problem raised by K. P. S. Bhaskara Rao and Rae Michael Shortt [Dissertationes Math. 372 (1998)] which we answer. We also briefly discuss generating the family of all subsets from rectangles.
