The embeddability ordering and order-resolutions.
by
Michael K Gormley
The Queen's University of Belfast
Coauthors: T.B.M. McMaster

A natural way to compare homeomorphism classes of topologies is to say that T₁ <= T₂ if and only if (X, T₁) is homeomorphic to a subspace of (X, T₂). A useful technique in the examination of the embeddability ordering is the ordersum construction whereby a collection of topological spaces indexed by a poset is coalesced into a single space containing homeomorphic copies of the original ones. This technique clearly reflects the notion of a topological resolution defined by Fedorcuk. We explore topological resolutions and define what we shall mean by an order-resolution, examining the connections between these ideas.

Date received: May 30, 2001