Bulletin of the American Mathematical Society ยท 1946 ยท 61 citations ยท 0 references
Natural SciencesMathematicsAlgebraSet TheoryTopologyConvex GeometryGeneral TopologyMetric GeometryTopological SpacesConvergenceEntire FunctionsMeasurable SpacesUniform Convergence
Introduction. The motive for investigating the class L w of functions belonging to all Z>-classes has no measure-theoretic origin: it was our desire to discover whether or not in every convex metric ring 1 R one could find a system { U] of convex neighborhoods of 0 having the property that/, g E U implies f g G U. We show here that Z, w has no proper convex open set U containing 0 and satisfying the relation UUQ U, thus supplying the desired counter-example.