On C-embedded subspaces of the Sorgenfrey plane

Abstract

We prove that every C * -embedded subset of S 2 is a hereditarily Baire subspace of R 2 . We also show that for a subspace E ⊆ {(x, −x) : x ∈ R} of the Sorgenfrey plane S 2 the following conditions are equivalent: 2010 MSC: 54C45; 54C20.