A topological space X is said to be splittable over a class of spaces P if for every A \subseteq X there exists continuous f:X --> Y in P such that f(A) \cap f(X \ A) is empty. A class of topological spaces P is said to be a splittability class if the spaces splittable over P are precisely the members of P. We extend the notion of splittability to partially ordered sets and consider splittability of some elementary posets. We identify precisely which subsets of a poset can be split along over an n -point chain. Using these results it is shown that the union of two splittability classes need not be a splittability class and a necessary condition for P to be a splittability class is given.

The research of the first author was supported by a distinction award scholarship from the Department of Education for Northern Ireland.

This article was published in a revised form. A. J. Hanna\ and\ T. B. M. McMaster, Splittability for partially ordered sets. Order {\bf 17} (2000), no.~4, 343--351 (2001); MR 2002a:54014