## Real Analysis Exchange

- Real Anal. Exchange
- Volume 31, Number 2 (2005), 547-551.

### Constructing Δ_{3}^{0} using topologically
restrictive countable disjoint unions.

#### Abstract

In a zero-dimensional Polish space, the Borel sets are generated from the clopen sets by repeatedly applying the operations of countable disjoint union and complementation. Here we look at topologically restrictive versions of the general countable disjoint union of sets, and obtain ``construction principles'' for $\mathbf{\Delta} \begin{smallmatrix} 0 \\ 3 \end{smallmatrix}$, i.e., sets which are both $\mathcal{F}_{\sigma\delta}$ and $\mathcal{G}_{\delta\sigma}$.

#### Article information

**Source**

Real Anal. Exchange, Volume 31, Number 2 (2005), 547-551.

**Dates**

First available in Project Euclid: 10 July 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.rae/1184104046

**Mathematical Reviews number (MathSciNet)**

MR2265795

**Subjects**

Primary: 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05] 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 03E15: Descriptive set theory [See also 28A05, 54H05]

**Keywords**

Borel sets Polish space separated union $\boldsymbol{\Delta}^{\boldsymbol{0}}_{\boldsymbol{3}}$

#### Citation

Dasgupta, Abhijit. Constructing Δ 3 0 using topologically restrictive countable disjoint unions. Real Anal. Exchange 31 (2005), no. 2, 547--551. https://projecteuclid.org/euclid.rae/1184104046