A Ramsey-type topological theorem (Q1862095)

Two proofs are given of the following theorem: for \(r,n\geq 2\) natural numbers if \(X\) is a monotonically normal, first countable space which is not left separated and if the \(r\)-tuples of \(X\) are coloured with \(n\) colours then there is a homogeneous convergent sequence in \(X\). Examples are given to show that the hypotheses cannot be relaxed significantly.