  In this paper, we contribute to the study of topological partition relations
for pairs of countable ordinals and prove that, for all integers $n \geq 3$,
\begin{align*} R^{cl}(\omega+n,3) &\geq \omega^2 \cdot n + \omega \cdot
(R(n,3)-n)+n\\ R^{cl}(\omega+n,3) &\leq \omega^2 \cdot n + \omega \cdot
(R(2n-3,3)+1)+1 \end{align*} where $R^{cl}(\cdot,\cdot)$ and $R(\cdot,\cdot)$
denote the closed Ramsey numbers and the classical Ramsey numbers respectively.
We also establish the following asymptotically weaker upper bound \[
R^{cl}(\omega+n,3) \leq \omega^2 \cdot n + \omega \cdot (n^2-4)+1\] eliminating
the use of Ramsey numbers. These results improve the previously known upper and
lower bounds.
