IJPAM: Volume 22, No. 1 (2005)

REAL ANALYTIC CONVEXITY ON DOMAINS OF
TOPOLOGICAL VECTOR SPACES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $V$ a locally convex and Hausdorff real topological vector space whose topology may be defined by a family of seminorms with finite-codimensional kernel, $\Omega \subset V$ a non-empty open subset, $S \subset
\Omega$ a closed subset of $\Omega$, and $P\in \Omega \backslash S$. Here we prove the existence a real analytic function $f: \Omega \to \mathbb {R}$ such that $f(P) > \sup _{Q\in S} \vert f(Q)\vert$.

Received: May 24, 2005

AMS Subject Classification: 32C05, 32D20, 46E99

Key Words and Phrases: real analytic function, real analytic function in infinite-dimensional topological vector spaces, topological vector space without a continuous norm, real analytic convex envelope

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 1