### Abstract

It is shown that the linear sum of two Borel subsets of the real line need not be Borel, even if one of them is compact and the other is Gδ. This result is extended to a fairly wide class of connected topological groups.

Original language | English |
---|---|

Pages (from-to) | 304-306 |

Number of pages | 3 |

Journal | Proceedings of the American Mathematical Society |

Volume | 25 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1970 |

### Fingerprint

### Keywords

- Absolute gδ
- Algebraically independent
- Analytic set
- Borel set
- Cantor set
- Complete metric space
- Connected topological group

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*25*(2), 304-306. https://doi.org/10.1090/S0002-9939-1970-0260958-1

**On the sum of two borel sets.** / Erdős, P.; Stone, A. H.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 25, no. 2, pp. 304-306. https://doi.org/10.1090/S0002-9939-1970-0260958-1

}

TY - JOUR

T1 - On the sum of two borel sets

AU - Erdős, P.

AU - Stone, A. H.

PY - 1970

Y1 - 1970

N2 - It is shown that the linear sum of two Borel subsets of the real line need not be Borel, even if one of them is compact and the other is Gδ. This result is extended to a fairly wide class of connected topological groups.

AB - It is shown that the linear sum of two Borel subsets of the real line need not be Borel, even if one of them is compact and the other is Gδ. This result is extended to a fairly wide class of connected topological groups.

KW - Absolute gδ

KW - Algebraically independent

KW - Analytic set

KW - Borel set

KW - Cantor set

KW - Complete metric space

KW - Connected topological group

UR - http://www.scopus.com/inward/record.url?scp=84968484121&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968484121&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1970-0260958-1

DO - 10.1090/S0002-9939-1970-0260958-1

M3 - Article

AN - SCOPUS:84968484121

VL - 25

SP - 304

EP - 306

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -