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 article, the authors construct an example of a rational metrizable continuum X containing a point x such that sup{nc(Y,x): x ϵ Y ⊆ X} = ω1.

TL;DR: For every non-zero ordinal γ with the usual order topology, K ( γ ) is normal iff cf γ = γ whenever γ is uncountable as mentioned in this paper.

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.