Dear Colleagues, The preprint mentioned below is available from my page on the WWW, http://www.andrew.cmu.edu/user/awodey/ Please let me know if you have difficulty obtaing or printing it, or if you would like to have a paper copy sent. Steve A. ******************************************************************************* "Topological representation of the lambda-calculus" S. Awodey Abstract: The lambda-calculus can be represented topologically by assigning certain spaces to the types and certain continuous maps to the terms. Using a recent result from topos theory, the usual calculus of lambda-conversion is shown to be deductively complete with respect to such topological semantics. It is also shown to be functionally complete, in the sense that there is always a ``minimal'' topological model, in which every continuous function is lambda-definable. These results subsume earlier ones using cartesian closed categories, as well as those employing so-called Henkin and Kripke lambda-models. *******************************************************************************