Weakly Borel-complete topological spaces
Weakly countably determined spaces of high complexity
We prove that there exist weakly countably determined spaces of complexity higher than coanalytic. On the other hand, we also show that coanalytic sets can be characterized by the existence of a cofinal adequate family of closed sets. Therefore the Banach spaces constructed by means of these families have at most coanalytic complexity.
When are Borel functions Baire functions?
The following two theorems give the flavour of what will be proved. Theorem. Let Y be a complete metric space. Then the families of first Baire class functions and of first Borel class functions from [0,1] to Y coincide if and only if Y is connected and locally connected.Theorem. Let Y be a separable metric space. Then the families of second Baire class functions and of second Borel class functions from [0,1] to Y coincide if and only if for all finite sequences of nonempty open subsets of Y there...
Zdeněk Frolík and the descriptive theory of sets and spaces
-discrete decomposability of completely additive families
-porosity is separably determined
We prove a separable reduction theorem for -porosity of Suslin sets. In particular, if is a Suslin subset in a Banach space , then each separable subspace of can be enlarged to a separable subspace such that is -porous in if and only if is -porous in . Such a result is proved for several types of -porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend a theorem...
Из принципа селектора для аналитических отношений эквивалентнисти не следует существование полного -упорядочения континуума
К вопросу Л.В.Келдыш о структуре борелевских множеств
О борелевских сечениях многозначных отображений.
О топологической силе теоретико-множественных операций
Характеризация -накрытия компакта