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Answer to a Question of S.~Rolewicz

  Published:2003-06-01
 Printed: Jun 2003
  • Félix Cabello Sánchez
  • Jesús M. F. Castillo
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Abstract

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, 46M15, 46A16, 46B20 show english descriptions None of the above, but in this section
Categories, functors {For $K$-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20}
Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
Geometry and structure of normed linear spaces
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
 

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