Monotone versions of δ-normality

According to Mack a space is countably paracompact if and only if its product with [0, 1] is delta-normal, i.e. any two disjoint closed sets, one of which is a regular G(delta)-set, call be separated. In studying monotone versions of countable paracompactness, one is naturally led to consider various monotone versions of delta-normality. Such properties are the subject of this paper. We look at how these properties relate to each other and prove a number of results about them, in particular, we provide a factorization of monotone normality in terms of monotone A-normality and a weak property that holds in monotonically normal spaces and in first countable Tychonoff spaces. We also discuss the productivity of these properties with a compact metrizable space. (C) 2009 Elsevier B.V. All rights reserved.