Abelian groups of continuous functions and their duals

Katsuya Eda, Shizuo Kamo, Haruto Ohta

研究成果: Article

4 引用 (Scopus)

抄録

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***.

元の言語English
ページ(範囲)131-151
ページ数21
ジャーナルTopology and its Applications
53
発行部数2
DOI
出版物ステータスPublished - 1993 11 26
外部発表Yes

Fingerprint

Abelian group
Continuous Function
Isomorphic
Subgroup
Subset
Subspace
Topology
Integer

ASJC Scopus subject areas

  • Geometry and Topology

これを引用

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

:: Topology and its Applications, 巻 53, 番号 2, 26.11.1993, p. 131-151.

研究成果: Article

Eda, Katsuya ; Kamo, Shizuo ; Ohta, Haruto. / Abelian groups of continuous functions and their duals. :: Topology and its Applications. 1993 ; 巻 53, 番号 2. pp. 131-151.
@article{7ec6104426cc4a97976315c0dd8cab71,
title = "Abelian groups of continuous functions and their duals",
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 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***.",
keywords = "Abelian group, Compact, Continuous function, Dual, N-compact, Reflixivity",
author = "Katsuya Eda and Shizuo Kamo and Haruto Ohta",
year = "1993",
month = "11",
day = "26",
doi = "10.1016/0166-8641(93)90133-X",
language = "English",
volume = "53",
pages = "131--151",
journal = "Topology and its Applications",
issn = "0166-8641",
publisher = "Elsevier",
number = "2",

}

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

AN - SCOPUS:33646016928

VL - 53

SP - 131

EP - 151

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 2

ER -