An interpolation lemma due to Kat etov is simpliied in order to make it more general and easier to use. Several results are established to illustrate applications of this lemma, including a characterization of monotonically normal spaces and a topology-free insertion theorem. We also prove that a topological space has an order-preserving insertion if and only if it is dominated by a collection ...

For a compact monotonically normal space X we prove: (1) X has a dense set of points with a well-ordered neighborhood base (and so X is co-absolute with a compact orderable space); (2) each point of X has a well-ordered neighborhood πbase (answering a question of Arhangel’skii); (3) X is hereditarily paracompact iff X has countable tightness. In the process we introduce weak-tightness, a notion...