Rothberger space information

In mathematics, a Rothberger space is a topological space that satisfies a certain a basic selection principle. A Rothberger space is a space in which for every sequence of open covers ${\mathcal {U}}_{1},{\mathcal {U}}_{2},\ldots$ of the space there are sets $U_{1}\in {\mathcal {U}}_{1},U_{2}\in {\mathcal {U}}_{2},\ldots$ such that the family $\{U_{n}:n\in \mathbb {N} \}$ covers the space.