Topological Vector Spaces and Convergence
by
Alexander Shibakov
Auburn Univeristy

We present a method of constructing topological groups and vector spaces with rich (or, surprisingly, none) convergence structure. This method allows us to construct (under CH) examples of a Frechet topological vector space with a sequential non Frechet square, sequential topological vector spaces of any sequential order, etc. Some results needed to make the technique work are fairly general and lead to positive results and interesting questions.

Date received: February 8, 1998