Published online by Cambridge University Press: 29 June 2016
Given a cardinal κ and a sequence ${\left( {{\alpha _i}} \right)_{i \in \kappa }}$ of ordinals, we determine the least ordinal β (when one exists) such that the topological partition relation
$$\beta \to \left( {top\,{\alpha _i}} \right)_{i \in \kappa }^1$$