Chains of strongly non-reflexive dual groups of integer-valued continuous functions
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- by Haruto Ohta PDF
- Proc. Amer. Math. Soc. 124 (1996), 961-967 Request permission
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.References
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Additional Information
- Haruto Ohta
- Affiliation: Faculty of Education, Shizuoka University, Ohya, Shizuoka, 422 Japan
- Email: h-ohta@ed.shizuoka.ac.jp
- 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.
- Communicated by: Franklin D. Tall
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 961-967
- MSC (1991): Primary 54C40, 20K20, 20K45
- DOI: https://doi.org/10.1090/S0002-9939-96-03360-6
- MathSciNet review: 1327034
Dedicated: Dedicated to Professor Shōzō Sasada on his $60$th birthday