International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 2, Pages 223-226
On Pervin's example concerning the connected-open topology
Pure Mathematics Department, Queen's University, Belfast BT7 1NN, Ireland
Received 5 May 1988
Copyright © 1990 T. B. M. McMaster. 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.
Irudayanathan and Naimpally  introduced a topology for function spaces (called the connected-open topology) which has the property that the connected functions form a closed set provided that the codomain is completely normal. Pervin  gave an example showing that the proviso cannot be weakened to normality. The purpose of this note is to point out a lacuna in his demonstration, and to re-establish the validity of the example.