A locally quasi-convex abelian group without a Mackey group topology
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Abstract:
We give the first example of a locally quasi-convex (even countable reflexive and $k_\omega$) abelian group $G$ which does not admit the strongest compatible locally quasi-convex group topology. Our group $G$ is the Graev free abelian group $A_G(\mathbf {s})$ over a convergent sequence $\mathbf {s}$.References
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Additional Information
- Saak Gabriyelyan
- Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, P.O. 653, Israel
- MR Author ID: 305815
- Email: saak@math.bgu.ac.il
- Received by editor(s): August 28, 2017
- Received by editor(s) in revised form: November 10, 2017
- Published electronically: February 28, 2018
- Communicated by: Heike Mildenberger
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3627-3632
- MSC (2010): Primary 22A10; Secondary 54H11
- DOI: https://doi.org/10.1090/proc/14020
- MathSciNet review: 3803686