Some properties of the Sorgenfrey line and related spaces

Any finite power S n of the Sorgenfrey line S has this covering property: if (x) is a neighborhood of x for each xeS n , then there is a closed discrete subset D of S n such that {(x): xeD} covers S n . No finite power of the Sorgenfrey line is homeomorphic to finite power of the irrational Sorgenfrey line. The Sorgenfrey plane is not the union of countably many nice subspaces.