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Abstract view

# Answer to a Question of S.~Rolewicz

We exhibit examples of $F$-spaces with trivial dual which are isomorphic to its quotient by a line, thus solving a problem in Rolewicz's {\it Metric Linear Spaces}.
 MSC Classifications: 46M99 - None of the above, but in this section 46M15 - Categories, functors {For $K$-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20} 46A16 - Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 46B20 - Geometry and structure of normed linear spaces