## Abstract

We consider amalgamation properties of convergent sequences in topological groups and topological vector spaces. The main result of this paper is that, for arbitrary topological groups, Nyikos's property α_{1.5} is equivalent to Arhangel'skiѤ's formally stronger property α_{1}. This result solves a problem of Shakhmatov (2002), and its proof uses a new perturbation argument. We also prove that there is a topological space X such that the space C_{p}(X) of continuous real-valued functions on X with the topology of pointwise convergence has Arhangel'skiѤ's property α_{1} but is not countably tight. This follows from results of Arhangel'skiѤ-Pytkeev, Moore and Todorčević, and provides a new solution, with stronger properties than the earlier solution, of a problem of Averbukh and Smolyanov (1968) concerning topological vector spaces.

Original language | English |
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Pages (from-to) | 281-293 |

Number of pages | 13 |

Journal | Fundamenta Mathematicae |

Volume | 232 |

Issue number | 3 |

DOIs | |

State | Published - 2016 |

### Bibliographical note

Publisher Copyright:© 2016 Instytut Matematyczny PAN.

## Keywords

- Amalgamation of convergent sequences
- L-space
- α space
- α space