On the complexity of subspaces of $S_{ω}$

• Autorzy: Carlos Uzcátegui
• Języki publikacji: EN

Abstrakty

EN

Let (X,τ) be a countable topological space. We say that τ is an analytic (resp. Borel) topology if τ as a subset of the Cantor set $2^X$ (via characteristic functions) is an analytic (resp. Borel) set. For example, the topology of the Arkhangel'skiĭ-Franklin space $S_ω$ is $F_{σδ}$. In this paper we study the complexity, in the sense of the Borel hierarchy, of subspaces of $S_ω$. We show that $S_ω$ has subspaces with topologies of arbitrarily high Borel rank and it also has subspaces with a non-Borel topology. Moreover, a closed subset of $S_ω$ has this property iff it contains a copy of $S_ω$.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 03E15: Descriptive set theory
• 54D55: Sequential spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 176
• Numer: 1
• Strony: 1-16

Daty

wydano

2003

Twórcy

autor

Carlos Uzcátegui

• Departamento de Matemáticas, Facultad de Ciencias, Universidad de Los Andes, Mérida 5101, Venezuela

Identyfikatory

DOI

10.4064/fm176-1-1