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

Abstract

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

Keywords

• Countable connected
• locally connected.