Let M<inf>X</inf> denote the ideal of meager subsets of a topological space X . We prove that if X is a completely metrizable space without isolated points, t[...]

Let denote the ideal of meager subsets of a topological space X. We prove that if X is a completely metrizable space without isolated points, then the smallest cardinalit[...]

The field of dynamical systems is generally interested in the study of collections of transformations acting upon some state space. In this work, we are primarily interes[...]

We show that CH implies every autohomeomorphism of N lifts through the natural projection to an autohomeomorphism of M. This complements a recent result of the second aut[...]

For which infinite cardinals κ is there a partition of the real line R into precisely κ Borel sets? Work of Lusin, Souslin, and Hausdorff shows that R can be partitioned [...]