Nonconvex linear topologies with the Hahn Banach extension property

 

David A. Gregory and Joel H. Shapiro

 

Proc. Amer. Math. Soc. 25 (1970), 902--905
 
Abstract: For a dual pair (E, E') of vector spaces we show that whenever the weak and Mackey topologies induced on E by the pairing are different then there is a nonconvex linear topolgy between them. In particular this provides a large class of nonconvex linear topolgies having the extension property guaranteed for locally convex spaces by the Hahn Banach Theorem.

 

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