(in Polish) Ideały miary i kategorii 1000-1M23ITM

1. Real line and related Polish spaces, the Cantor and Baire spaces. Elements of descriptive set theory: borel and analytic sets. Perfect sets and the perfect set property for classes of subsets of Polish spaces.

2. Ideals of measure and category as c.c.c. ideals with Borel bases. Quotient algebras of Borel sets modulo an ideal, Sikorski's theorem. Baire property as a "category" version of measurability. The Kuratowski-Ulam Theorem as a counterpart of the Fubini Theorem. Orthogonality of ideals of measure and category. Erdős-Sierpiński duality theorem (under CH), non-existence of an additive Erdős-Sierpiński mapping.

3. Theorems and constructions regarding non-measurable sets or sets w/o the Baire property, e.g. The Four Poles Theorem. Nonmeasurable algebraic sums of sets from the ideal.

4. Cardinal characteristics of the ideals of measure and category and the inequalities between them (e.g. Rothberger's inequality). Cichoń's diagram.

5, Universal Measure Zero sets and their catgeory counterparts: Always of First Category Sets and Universally of First Category Sets. and their properties, e.g. the existence of uncountable sets with these properties.

6. Strong Measure Zero sets, their metric definition and the characterization by Galvin-Mycielski-Solovay. Their category counterparts - strongly meager and very meager sets. Sets with Rothberger's property and other related classes. Luzin and Sierpiński sets. Information about the Borel Conjecture and the Dual Borel Conjecture.