On the closed Ramsey numbers Rcl(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 bound:eliminating the use of Ramsey numbers. These results improve the previously known upper and lower bounds.