International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 3, Pages 459-462
doi:10.1155/S0161171298000635

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