### Abstract

Let A^{*} = Hom (A, Z) for an Abelian group A, were Z is the group of integers. A^{*} is endowed with the topology as a subspace of Z^{A}. Then, for a 0-dimensional space X and an infinite cardinal κ the following are equivalent. (1) There exists a free summand of C(X, Z) of rank κ; (2) there exists a subgroup of C(X, Z)^{*} isomorphic to Z^{κ}; (3) there exists a compact subset K of β_{N}X with w(K)≥κ; (4) there exists a compact subset K of C(X, Z)^{*} with w(K)≥κ. There exist groups A such that A^{*} is a subgroup of Z^{N} and A^{*} is not isomorphic to A^{***}.

Original language | English |
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Pages (from-to) | 131-151 |

Number of pages | 21 |

Journal | Topology and its Applications |

Volume | 53 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1993 Nov 26 |

Externally published | Yes |

### Keywords

- Abelian group
- Compact
- Continuous function
- Dual
- N-compact
- Reflixivity

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Eda, K., Kamo, S., & Ohta, H. (1993). Abelian groups of continuous functions and their duals.

*Topology and its Applications*,*53*(2), 131-151. https://doi.org/10.1016/0166-8641(93)90133-X