# IJPAM: Volume 27, No. 2 (2006)

TOPOLOGICAL VECTOR SPACES WITHOUT
REAL ANALYTIC -NORMS''

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]

Abstract.Here we point out the following consequences of a previous result of mine. Let be a Hausdorff and locally convex topological vector space without any continuous norm and an -norm defining the topology of . Then there is no pair with an open neighborhood of and a real analytic function such that and the sets form a fundamental system of open neighborhoods of in . Furthermore, there is no strictly increasing function such that is real analytic.