Ordered Spaces all of whose Continuous Images are Normal

Abstract

Some spaces, such as compact Hausdorff spaces, have the property that every regular continuous image is normal. In this paper, we look at such spaces. In particular, it is shown that if a normal space has finite Stone-Cech remainder, then every continuous image is normal. A consequence is that every continuous image of a Dedekind complete linearly ordered topological space of uncountable cofinality and coinitiality is normal. The normality of continuous images of other ordered spaces is also discussed.