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Keywords:
Hahn-Banach extension property; topological vector space
Hahn-Banach extension property; topological vector space
Summary:
An elementary construction for an abundance of vector topologies $\xi $ on a fixed infinite dimensional vector space $E$ such that $(E,\xi )$ has not the Hahn-Banach extension property but the topological dual $(E,\xi )'$ separates points of $E$ from zero is given.
References:
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[4] Klee V.: Exotic topologies for linear spaces. Proc. Symposium on General Topology and its Relations to Modern Algebra, Prague, 1961. MR 0154088 | Zbl 0111.10701
[5] Shapiro J.H.: Examples of proper closed weakly dense subspaces in non-locally convex $F$-spaces. Israel J. Math. 7 (1969), 369-380. MR 0257696 | Zbl 0202.39303
[6] Wilansky A.: Topics in Functional Analysis. Springer Verlag 45 (1967). MR 0223854 | Zbl 0156.36103
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