### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Topology and its Applications*,

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

**Prime subspaces in free topological groups.** / Eda, Katsuya; Ohta, Haruto; Yamada, Kohzo.

Research output: Contribution to journal › Article

*Topology and its Applications*, vol. 62, no. 2, pp. 163-171. https://doi.org/10.1016/0166-8641(94)00030-7

}

TY - JOUR

T1 - Prime subspaces in free topological groups

AU - Eda, Katsuya

AU - Ohta, Haruto

AU - Yamada, Kohzo

PY - 1995/3/24

Y1 - 1995/3/24

N2 - 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 ω1 + 1, this is not true. If P = ω1, this holds for F(X) but is independent of ZFCfor A(X).

AB - 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 ω1 + 1, this is not true. If P = ω1, this holds for F(X) but is independent of ZFCfor A(X).

KW - Convergent sequenc

KW - Free Abelian topological group

KW - Free topological group

KW - Prime space

KW - Self-embeddable space

KW - Symmetric product

UR - http://www.scopus.com/inward/record.url?scp=0037818767&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037818767&partnerID=8YFLogxK

U2 - 10.1016/0166-8641(94)00030-7

DO - 10.1016/0166-8641(94)00030-7

M3 - Article

AN - SCOPUS:0037818767

VL - 62

SP - 163

EP - 171

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 2

ER -