IS THE CLUSTER TEMPERATURE FUNCTION A RELIABLE TEST FOR OMEGA(0)

We discuss the evolution of the cluster temperature function (TF) in d ifferent scenarios for structure formation. We use the commonly adopte d procedure of fitting the model parameters to the local TF data to fi nd the best-fit values and, most of all, the associated statistical er rors. These errors yield an uncertainty in the prediction of the TF ev olution. We conclude that, at the moment, observations of cluster temp eratures at z less than or similar to 0.5 could provide only a weak te st for Ohm(0).