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Proceedings of the American Mathematical Society

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Note on compatible vector topologies


Author: Jerzy Kąkol
Journal: Proc. Amer. Math. Soc. 99 (1987), 690-692
MSC: Primary 46A15
DOI: https://doi.org/10.1090/S0002-9939-1987-0877041-7
MathSciNet review: 877041
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Abstract: Let $ \left\langle {X,Y} \right\rangle $ be a dual pair. Then $ X$ admits the finest locally convex topology $ \mu $ which is compatible with $ \left\langle {X,Y} \right\rangle $. In contrast, it is proved that there is no finest vector topology on $ X$ which is compatible with $ \left\langle {X,Y} \right\rangle $ provided $ X$ contains a $ \mu $-dense subspace of infinite codimension.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0877041-7
Keywords: Topological vector space, locally convex space, dual-less space, dual pair
Article copyright: © Copyright 1987 American Mathematical Society