On Pervin's example concerning the connected-open topology

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.