Resumen de Everywhere meagre and everywhere null sets

Jan Kraszewski

• We introduce new classes of small subsets of the reals (connected with Mycielski ideals), having natural combinatorial definitions, namely everywhere meagre and everywhere null sets. We investigate properties of these sets, in particular we show that these classes are closed under taking products and projections. We also prove several relations between these classes and other well-known classes of small subsets of the reals (e.g. universally meagre sets or strongly meagre sets).