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International Journal of Mathematics and Mathematical Sciences
Volume 21, Issue 3, Pages 459-462
http://dx.doi.org/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 Hindawi Publishing Corporation. 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.