More things I don't know about finite spaces.
by
Brian McMaster
Queen's University Belfast
Coauthors: Alan Hanna (DART U.K.)

A space X is splittable over a space Y when, for each subset A of X, there is a continuous map from X to Y under which the images of A and of its complement are disjoint. The concept is due to Arhangel'skii, who generally includes in the definition that the map be surjective.

When each of two spaces is splittable over the other, they are indistinguishable from the point of view of splittability. Even in the [apparently trivial] case of finite spaces of a given size, this equivalence relation gives rise [at present, anyway] to more ill-defined questions than tidy answers. We shall review some of them.

Date received: September 1, 2000