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A locally quasi-convex abelian group without a Mackey group topology

Author: Saak Gabriyelyan
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 22A10; Secondary 54H11
Published electronically: February 28, 2018
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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}$.

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Additional Information

Saak Gabriyelyan
Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, P.O. 653, Israel

Keywords: The Graev free abelian topological group, Mackey group topology
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
Article copyright: © Copyright 2018 American Mathematical Society

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