Disconnectedness Properties in Hyperspaces, Spaces of Remote Points and Countable Dense Homogeneous Spaces

TL;DR: In this paper, the authors studied the disconnectedness properties of Hausdorff spaces with respect to extremal disconnectedness and hereditary disconnectedness, and showed that if the quotient of a quotient $X/F$ is hereditarily disconnected, then it cannot be reversed.

TL;DR: In this paper, the Banach-Mazur game was extended to the case of continuous functions, and the notion of metric spaces was introduced for continuous functions in the space of measurable sets.

TL;DR: In this article, the authors present a complete solution to the topological classification problem for topological groups with compact-open topology, and show that these groups are homeomorphic to Erdos spaces.

TL;DR: In this paper, it was shown that if an element M of JJ contains no open subset imbeddable in the plane then M is the universal curve and SU is the subclass of M consisting of those elements of M having no local cut points.

TL;DR: In this paper, the authors present a model of set theory in which there are noP-points in βN/N and show that this model is consistent with Shelah's example.