  Dialectica categories are a very versatile categorical model of linear logic.
These have been used to model many seemingly different things (e.g., Petri nets
and Lambek's calculus). In this note, we expand our previous work on fuzzy
petri nets to deal with fuzzy topological systems. One basic idea is to use as
the dualizing object in the Dialectica categories construction, the unit real
interval [0,1], which has all the properties of a {\em lineale}. The second
basic idea is to generalize Vickers's notion of a topological system.
