On the closed Ramsey numbers $R^{cl}(ω+n,3)$

Abstract

In this paper, we contribute to the study of topological partition relations for pairs of countable ordinals and prove that, for all integers n ≥ 3,where R cl (•, •) and R(•, •) denote the closed Ramsey numbers and the classical Ramsey numbers respectively. We also establish the following asymptotically weaker upper boundeliminating the use of Ramsey numbers. These results improve the previously known upper and lower bounds.