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

DOI:
https://doi.org/10.1090/S0002-9939-96-03360-6

MathSciNet review:
1327034

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Abstract | References | Similar Articles | Additional Information

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 consisting of ordinals of cofinality for each , then there exist abelian groups such that and for each . (2) There exist abelian groups such that for each and for each . The groups are the groups of -valued continuous functions on a topological space and their dual groups.

**1.**K. Eda and H. Ohta,*On abelian groups of integer-valued continuous functions, their -duals and -reflexivity*, Abelian Group Theory (R. Göbel and E. Walker, eds.), Gordon and Breach, London, 1985, pp. 241--257. MR**90f:20081****2.**K. Eda, T. Kiyosawa and H. Ohta,*-compactness and its applications*, Topics in General Topology (K. Morita and J. Nagata, eds.), North-Holland, Amsterdam, 1989, pp. 459--521. MR**95m:54018****3.**K. Eda, S. Kamo and H. Ohta,*Abelian groups of continuous functions and their duals*, Topology and its Appl.**53**(1993), 131--151. MR**94m:20108****4.**P. C. Eklof and A. H. Mekler,*Almost Free Modules, Set-theoretic Methods*, North-Holland, Amsterdam, 1990. MR**92e:20001****5.**P. C. Eklof, A. H. Mekler and S. Shelah,*On strongly-non-reflexive groups*, Israel J. Math.**59**(1987), 283--298. MR**89c:20080****6.**G. Schlitt,*Sheaves of abelian groups and the quotients*, J. Algebra**158**(1993), 50-60. MR**94e:20072**

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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

DOI:
https://doi.org/10.1090/S0002-9939-96-03360-6

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