Ae. Mccluskey et Tbm. Mcmaster, Representing quasi-orders by embeddability ordering of families of topological spaces, P AM MATH S, 127(5), 1999, pp. 1275-1279
An elementary argument constructs, for each cardinal alpha, a topological s
pace whose subspaces, ordered by homeomorphic embeddability, can model ever
y partial order on alpha-many points. We show how to modify this procedure
to deal also with quasi-orders (where the antisymmetry condition may fail),
obtaining an initial estimate of the cardinality of the space then require
d.