On C-embedded subspaces of the Sorgenfrey plane

Abstract

[EN] We prove that every C∗ -embedded subset of S2 is a hereditarily Baire subspace of R2. We also show that for a subspace E ⊆ {(x, −x) : x ∈ R} of the Sorgenfrey plane S2 the following conditions are equivalent: (i) E is C-embedded in S2; (ii) E is C∗-embedded in S2; (iii) E is a countable Gδ -subspace of R2 and (iv) E is a countable functionally closed subspace of S2.