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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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Pretopologies and geometric Hahn-Banach theorem
by
Josep Rubió-Massegú
Universidad Politécnica de Cataluña
Coauthors: Ramon Miralles Rafart (Universidad Nacional de Educación a Distancia), Pere Rubió Díaz (Universidad Politécnica de Cataluña)

We study different pretopologies which are compatible with the structure of a vector space E. Our aim is to study the classical concepts of algebraic interior and algebraic closure of a set in the frame of pretopologies. The relation between the algebraic concepts and the topological ones for different pretopologies is analyzed. The geometric Hahn-Banach theorem is studied for different pretopologies. It holds for pretopologies which are coarser than the algebraic pretopology. However, the theorem does not hold in general for pretopologies which are finer than the algebraic one.

(P)

Date received: April 15, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caey-78.