## Journal of Symbolic Logic

### Recursive Constructions in Topological Spaces

#### Abstract

We study topological constructions in the recursion theoretic framework of the lattice of recursively enumerable open subsets of a topological space $X$. Various constructions produce complemented recursively enumerable open sets with additional recursion theoretic properties, as well as noncomplemented open sets. In contrast to techniques in classical topology, we construct a disjoint recursively enumerable collection of basic open sets which cannot be extended to a recursively enumerable disjoint collection of basic open sets whose union is dense in $X$.

#### Article information

Source
J. Symbolic Logic, Volume 44, Issue 4 (1979), 609-625.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183740469

Mathematical Reviews number (MathSciNet)
MR550389

Zentralblatt MATH identifier
0427.03035

JSTOR