Menger space

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 of the space there are finite sets such that the family covers the space. History In 1924, Karl Menger introduced the following basis property for metric spaces: Every basis of the topology contains a countable family of sets with vanishing diameters that covers the space. Soon thereafter, Witold Hurewicz observed that Menger's basis property can be reformulated to the above form using sequences of open covers. Menger's conjecture