Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: perfect set

Sortuj według:

Ogranicz wyniki do:

Ramsey, Lebesgue, and Marczewski sets and the Baire property

100%

Reardon P.

Fundamenta Mathematicae

1996

tom 149

nr 3

191-203

We investigate the completely Ramsey, Lebesgue, and Marczewski σ-algebras and their relations to the Baire property in the Ellentuck and density topologies. Two theorems concerning the Marczewski σ-algebra (s) are presented. THEOREM. In the density topology D, (s) coincides with the σ-algebra of Lebesgue measurable sets. THEOREM. In the Ellentuck topology on $[ω]^ω$, $(s)_0$ is a proper subset of the hereditary ideal associated with (s). We construct an example in the Ellentuck topology of a set which is first category and measure 0 but which is not $B_r$-measurable. In addition, several theorems concerning perfect sets in the Ellentuck topology are presented. In particular, it is shown that there exist countable perfect sets in the Ellentuck topology.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Reardon P.

1 1996

Wyniki wyszukiwania

Ramsey, Lebesgue, and Marczewski sets and the Baire property