A dichotomy theorem for the Ellentuck topology.

Abstract

Results are deduced from the following dichotomy which reduces descriptive properties concerning the Ellentuck topology to two well-known examples. Theorem:Every nonempty perfect set in the Ellentuck topology contains a closed copy of the Sorgenfrey line or a closed copy of the rational numbers. This leads to a Marczewski-Burstin representation for Marczewski sets in the Ellentuck topology.