Seminarium:
Topologia
Osoba referująca:
Piotr Szewczak (UKSW)
Data:
wtorek, 6. Czerwiec 2023 - 17:15
Sala:
A.4.1 C-19 (Politechnika Wrocławska)
Opis:
A set of reals X is Menger if for any countable sequence of open covers of
X one can pick finitely many elements from every cover in the sequence such
that the chosen sets cover X. Any set of reals of cardinality smaller than
the dominating number d is Menger and there is a non-Menger set of
cardinality d. By the result of Bartoszyński and Tsaban, in ZFC, there is a
totally imperfect (with no copy of the Cantor set inside) Menger set of
cardinality d. We solve a problem, whether there is such a set of
cardinality continuum. Using an iterated Sacks forcing and topological
games we prove that it is consistent with ZFC that d