Subspaces of the Sorgenfrey Line

We study three problems which involve the nature of subspaces of the Sorgenfrey Line S. It is shown that no integer power of an uncountable subspace of S can be embedded in a smaller power of S. We review the known results about the existence of uncountable X ⊆ S where X2 is Lindelöf. These results about Lindelöf powers are quite set-theoretic. A descriptive characterization is given of those subspaces of S which are homeomorphic to S. We show that a nonempty subspace Z ⊆ S is homeomorphic to S if and only if Z is dense-in-itself and is both Fσ and Gδ in S.