On homeomorphisms of spaces $I\times[1,\alpha]$ with the Sorgenfrey topology

In this paper, a topological classification of spaces $I\times[1,\alpha]$ is presented. Here, $\alpha$ is an arbitrary ordinal and the semi-interval $I=(0,1]$ is equipped with the Sorgenfrey topology. It is proved that the space $I\times[1,\alpha]$ is homeomorphic to the space $I\times[1,\beta]$ if and only if $\alpha\le\beta<\alpha\cdot\omega$.