Chu-ing on Sierpinski

**Abstract:**

In this talk, based on joint work with Michael Barr and Bob Raphael,
the category of vector spaces over a fixed field
is used to illustrate (and, in effect, to define) the notion of a
closed symmetric monodial category. Similarly,
Mackey's approach to topological vector spaces is used to illustrate
the chu construction.

We use this construction to explore the category of topological sup
semilattices by examining the continuous morphisms
into the two-point semilattice with the Sierpinski topology (with the
bottom element open). We obtain some duality
results and characterize the reflexive objects, which form a
*-autonomous category