We present a ZFC construction of a non-meager filter which fails to be countable dense homogeneous. This answers a question of Hernández-Gutiérrez and Hrušák. The method of the proof also allows us to obtain for any n \in \omega \cup \{ \infty \} an n-dimensional metrizable Baire topological group which is strongly locally homogeneous but not countable dense homogeneous.
COBISS.SI-ID: 16962905
We prove that under certain set-theoretic assumptions every productively Lindelöf space has the Hurewicz covering property, thus improving upon some earlier results of Aurichi and Tall.
COBISS.SI-ID: 16975961
We settle all problems concerning the additivity of the Gerlits-Nagy property and related additivity numbers posed by Scheepers in his tribute paper to Gerlits. We apply these results to compute the minimal number of concentrated sets of reals (in the sense of Besicovitch) whose union, when multiplied with a Gerlits-Nagy space, need not have Rothberger's property. We apply these methods to construct a large family of spaces whose product with every Hurewicz space has Menger's property. Our applications extend earlier results of Babinkostova and Scheepers.
COBISS.SI-ID: 17010521