Menger space

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In mathematics, a Menger space is a topological space that satisfies a certain basic selection principle that generalizes σ-compactness. A Menger 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 the family ${\displaystyle {\mathcal {F}}_{1}\cup {\mathcal {F}}_{2}\cup \cdots }$ covers the space.