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

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Geometry and Topology

### Cite this

*Topology and its Applications*,

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

**Abelian groups of continuous functions and their duals.** / Eda, Katsuya; Kamo, Shizuo; Ohta, Haruto.

Research output: Contribution to journal › Article

*Topology and its Applications*, vol. 53, no. 2, pp. 131-151. https://doi.org/10.1016/0166-8641(93)90133-X

}

TY - JOUR

T1 - Abelian groups of continuous functions and their duals

AU - Eda, Katsuya

AU - Kamo, Shizuo

AU - Ohta, Haruto

PY - 1993/11/26

Y1 - 1993/11/26

N2 - 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 ZA. 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 Zκ; (3) there exists a compact subset K of βNX 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 ZN and A* is not isomorphic to A***.

AB - 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 ZA. 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 Zκ; (3) there exists a compact subset K of βNX 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 ZN and A* is not isomorphic to A***.

KW - Abelian group

KW - Compact

KW - Continuous function

KW - Dual

KW - N-compact

KW - Reflixivity

UR - http://www.scopus.com/inward/record.url?scp=33646016928&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646016928&partnerID=8YFLogxK

U2 - 10.1016/0166-8641(93)90133-X

DO - 10.1016/0166-8641(93)90133-X

M3 - Article

VL - 53

SP - 131

EP - 151

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 2

ER -