Hurewicz space

In mathematics, a Hurewicz space is a topological space that satisfies a certain basic selection principle that generalizes σ-compactness. A Hurewicz space is a space in which for every sequence of open covers ${\displaystyle {\mathcal {U}}_{1},{\mathcal {U}}_{2},\ldots }$ of the space there are finite sets ${\displaystyle {\mathcal {F}}_{1}\subset {\mathcal {U}}_{1},{\mathcal {F}}_{2}\subset {\mathcal {U}}_{2},\ldots }$ such that every point of the space belongs to all but finitely many sets ${\displaystyle \bigcup {\mathcal {F}}_{1},\bigcup {\mathcal {F}}_{2},\ldots }$ .