International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 1, Pages 1-8
doi:10.1155/S0161171289000013
Abstract
Closed and nowhere dense subsets which coincide with the points of
discontinuity of real-valued functions with a closed graph on spaces which are not
necessarily perfectly normal are investigated. Certain Gδ
subsets of completely
regular and normal spaces are characterized. It is also shown that there exists a
countable connected Urysohn space X with the property that no closed and nowhere
dense subset of X coincides with the points of discontinuity of a real-valued
function on X with a closed graph.