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 | 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.**Katsuya Eda and Haruto Ohta,*On abelian groups of integer-valued continuous functions, their 𝑍-duals and 𝑍-reflexivity*, Abelian group theory (Oberwolfach, 1985) Gordon and Breach, New York, 1987, pp. 241–257. MR**1011316****2.**Strashimir G. Popvassilev,*Hereditarily semiregular, compact 𝑇₁ space that is not Hausdorff*, Questions Answers Gen. Topology**13**(1995), no. 1, 83–85. MR**1315474****3.**Katsuya Eda, Shizuo Kamo, and Haruto Ohta,*Abelian groups of continuous functions and their duals*, Topology Appl.**53**(1993), no. 2, 131–151. MR**1247673**, 10.1016/0166-8641(93)90133-X**4.**Paul C. Eklof and Alan H. Mekler,*Almost free modules*, North-Holland Mathematical Library, vol. 46, North-Holland Publishing Co., Amsterdam, 1990. Set-theoretic methods. MR**1055083****5.**Paul C. Eklof, Alan H. Mekler, and Saharon Shelah,*On strongly nonreflexive groups*, Israel J. Math.**59**(1987), no. 3, 283–298. MR**920497**, 10.1007/BF02774142**6.**G. Schlitt,*Sheaves of abelian groups and the quotients 𝐴**/𝐴*, J. Algebra**158**(1993), no. 1, 50–60. MR**1223667**, 10.1006/jabr.1993.1123

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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:
http://dx.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