Monotonically normal spaces

Abstract

This paper begins the study of monotone normality, a common property of linearly ordered spaces and of Borges’ stratifiable spaces. The concept of monotone normality is used to give necessary and sufficient conditions for stratifiability of a T 1 {T_1} -space, to give a new metrization theorem for p-spaces with G δ {G_\delta } -diagonals, and to provide an easy proof of a metrization theorem due to Treybig. The paper concludes with a list of examples which relate monotone normality to certain familiar topological properties.