The quasi-Rothberger property of linearly ordered spaces

A space X is said to be quasi-Rothberger if for each closed set F⊂X and each sequence {Un:n∈N} of covers of F by sets open in X, there is a Un∈Un for each n∈N such that F⊂⋃n∈NUn‾. In this article, we give necessary and sufficient conditions of the quasi-Rothberger property of linearly ordered spaces.