Mel Hochster

Holger Brenner has recently introduced the notion of the continuous closure of an ideal in a finitely generated reduced algebra R over the complex numbers C. It is the contracted expansion of the ideal from the ring of all continuous C-valued functions on the algebraic set associated with R. We discuss Brenner's results as well as some new results connecting this sort of closure with algebraically defined closures. The new results are joint work with Neil Epstein.