Representing quasi-orders by embeddability ordering of families of topological spaces
Aisling E. McCluskey, T. B. M. McMaster · Proceedings of the American Mathematical Society · 1999
An elementary argument constructs, for each cardinal α \alpha , a topological space whose subspaces, ordered by homeomorphic embeddability, can model every partial order on α \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 required.