Carry on cleaving
by
A.J. Hanna
The Queen's University of Belfast
Coauthors: T.B.M. McMaster

A partial order X is splittable over a partial order Y if for every subset A of X there exists an order-preserving mapping f:X --> Y such that f^-1f(A)=A. Suppose that \alpha copies of a space X can be disjointly embedded into a single copy of X. It is clear that the disjoint sum of (at least) \alpha copies of X will split over a single copy of X. We define a cardinal function sc(X) (the `splittability ceiling' for X) to be the least cardinal \beta such that the disjoint sum of \beta copies of X fails to split over a single copy of X. We allow sc(X)=\infty to cover the case where arbitrarily many disjoint copies may be split. We investigate this cardinal function, with respect to (linear) partial orders.

Date received: July 28, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabl-06.