Approach vector spaces
by
Verwulgen Stijn
Coauthors: R. Lowen

Approach spaces, introduced by R. Lowen, are a supercategory of topological and metric spaces. They are useful to generalize both metric and topological structures on vector spaces.

Looking in a certain way to topological vector spaces, we are invited to numerify the axioms matching the topological and algebraic part. In this way we arrive at metric vector spaces and the fact that they generate the topological vector spaces.

Imposing a convexity condition to the numerical information we get, in the metric case a pseudo-norm and in the topological case a locally convex topology.

Date received: June 26, 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 # caeq-53.