On countable connected Hausdorff spaces in which the intersection of every pair of connected subsets in connected

摘要

We prove that a countable connected Hausdorff space in which the intersection ofevery pair of connected subsets is connected, cannot be locally connected, and also that everycontinuous function from a countable connected, locally connected Hausdorff space, to a countableconnected Hausdorff space in which the intersection of every pair of connected subsets is connected,is constant.