On Kuratowski partitions in the Marczewski and Laver structures and Ellentuck topology

Abstract

Abstract In this paper, we study the question of the existence of Kuratowski partitions in tree structures and Ellentuck topology. On the examples of Marczewski and Laver structures and the structure of Ellentuck topology, we show that non-small sets of these structures do not admit Kuratowski partitions.