Darboux Baire 1 function and the cofinality of the ideal of meager sets
by
Francis Jordan
West Virginia University

Let D subset or equal \real^\real and B₁ subset or equal \real^\real denote the collections of Darboux functions and Baire Class 1 functions. It is known that for any finite collection G₁ subset or equal B₁ there is an f in D \cap B₁ such that f+G subset or equal D \cap B₁. We sharpen this result by finding the minimum cardinality of a family H subset or equal B₁ \cap D such that for any finite collection G subset or equal B₁ there is an h in H such that h+G subset or equal D \cap B₁. This cardinal turns out to be the cofinality of the ideal of meager subsets of \real. Similar results are found for the classes of quasi-continuous and cliquish functions.

Date received: January 26, 1998