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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 U 1 , U 2 , … {\displaystyle {\mathcal {U}}_{1},{\mathcal {U}}_{2},\ldots } of the space there are sets U 1 ∈ U 1 , U 2 ∈ U 2 , … {\displaystyle U_{1}\in {\mathcal {U}}_{1},U_{2}\in {\mathcal {U}}_{2},\ldots } such that the family { U n : n ∈ N } {\displaystyle \{U_{n}:n\in \mathbb {N} \}} covers the space.