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 in connected
Department of Mathematics, University of Patras, Patras 26110, Greece
Received 2 July 1996; Revised 28 December 1996
Copyright © 1998 V. Tzannes. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.