Some properties of the sorgenfrey line and related spaces

Abstract

Any finite power Snof the Sorgenfrey line S has this covering property: if ψ(x) is a neighborhood of x for each xϵSn, then there is a closed discrete subset D of Sn such that {ψ(x): xϵD} covers Sn. 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. © 1979 by Pacific Journal of Mathematics.