Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Chains of strongly non-reflexive dual groups
of integer-valued continuous functions

Author: Haruto Ohta
Journal: Proc. Amer. Math. Soc. 124 (1996), 961-967
MSC (1991): Primary 54C40, 20K20, 20K45
MathSciNet review: 1327034
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Abstract: Answering a question of Eklof-Mekler (Almost free modules, set-theoretic methods, North-Holland, Amsterdam, 1990), we prove: (1) If there exists a non-reflecting stationary set of $\omega _{i}$ consisting of ordinals of cofinality $\omega $ for each $1 < i < \omega $, then there exist abelian groups $A_{n} (n \in {\mathbb{Z}})$ such that $A_{n}^{\ast } \cong A_{n+1}$ and $A_{n} \not \cong A_{n+2}$ for each $n \in {\mathbb{Z}}$. (2) There exist abelian groups $A_{n} (n \in {\mathbb{Z}})$ such that $A_{n}^{\ast } \cong A_{n+1}$ for each $n \in {\mathbb{Z}}$ and $A_{n} \not \cong A_{n+2}$ for each $n < 0$. The groups $A_{n}$ are the groups of $\mathbb{Z}$-valued continuous functions on a topological space and their dual groups.

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Additional Information

Haruto Ohta
Affiliation: Faculty of Education, Shizuoka University, Ohya, Shizuoka, 422 Japan

Keywords: Abelian group, continuous function, dual group, reflexivity, strong non-reflexivity, $\mathbb{Z}$-compact
Received by editor(s): July 6, 1994
Additional Notes: Research partially supported by Grant-in-Aid for Scientific Research No. 06640125, Ministry of Education, Science and Culture.
Dedicated: Dedicated to Professor Shōzō Sasada on his $60$th birthday
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1996 American Mathematical Society