International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 2, Pages 223-226
doi:10.1155/S0161171290000333
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.
Abstract
Irudayanathan and Naimpally [1] 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 [2] 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.