Computability of a topological poset

Computability of a topological poset Article

Gillam, WD. (2006). Computability of a topological poset . TOPOLOGY AND ITS APPLICATIONS, 153(7), 1132-1140. 10.1016/j.topol.2005.03.004

For subspaces X and Y of ℚ the notation X ≤h Y means that X is homeomorphic to a subspace of Y and X ∼ Y means X ≤hY ≤h X. The resulting set P(ℚ)/∼ of equivalence classes X̄ = {Y ⊆ ℚ: Y ∼ X} is partially-ordered by the relation X̄ ≤h Ȳ if X ≤h Y. In a previous paper by the author it was established that this poset is essentially determined by considering only the scattered X ⊆ ℚ of finite Cantor-Bendixson rank. Results from that paper are extended to show that this poset is computable. © 2005 Elsevier B.V. All rights reserved.