### Abstract

Let F(X) (A(X)) be the free (Abelian) topological group over X. We prove: If P is one of the spaces R, Q, R, Q, βω, βω ω and 2^{/gk} for an infinite κ and if F(X) or A(X) contains a copy of P, then X contains a copy of P. If P is the one-point compactification of an infinite discrete space or ω_{1} + 1, this is not true. If P = ω_{1}, this holds for F(X) but is independent of ZFCfor A(X).

Original language | English |
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Pages (from-to) | 163-171 |

Number of pages | 9 |

Journal | Topology and its Applications |

Volume | 62 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1995 Mar 24 |

### Keywords

- Convergent sequenc
- Free Abelian topological group
- Free topological group
- Prime space
- Self-embeddable space
- Symmetric product

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Eda, K., Ohta, H., & Yamada, K. (1995). Prime subspaces in free topological groups.

*Topology and its Applications*,*62*(2), 163-171. https://doi.org/10.1016/0166-8641(94)00030-7