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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