Instituto de Matematicas, Unidad Morelia, Nicolas Romero 150
Col Centro, Morelia, Mexico
Faculty of Mathematics and Computer Science, Vrije Universiteit,
De Boelelaan 1081 a, 1081 HV Amsterdam, The Netherlands
Abstract. We show that a family U of open subsets of a subset X of a hereditarily normal paracompact space P which is locally finite in P admits a locally finite open extension V in P which is similar to U. We apply this fact to prove an extension theorem for overlays over hereditarily paracompact spaces.
1991 Mathematics Subject Classification. 54D15, 54D20, 54C56.
Key words and phrases. Hereditarily normal space, hereditarily paracompact space, similar families, overlay.