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

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

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

M3 - Article

AN - SCOPUS:33646016928

SN - 0166-8641

VL - 53

SP - 131

EP - 151

JO - Topology and its Applications

JF - Topology and its Applications

IS - 2

ER -