The product of two ordinals is hereditarily countably metacompact (Q675107)

Let \(\mu\) be an ordinal number. We consider \(\mu\) as the space of ordinal numbers less than \(\mu\) with the order topology. It is shown that any subspace of \(\mu \times \mu\) is countably metacompact, which gives a positive answer to the question in [\textit{N. Kemoto, H. Ohta} and \textit{K. Tamano}, Topology Appl. 45, No. 3, 245-260 (1992; Zbl 0789.54006)] whether the product of any two subspaces of \(\mu\) is countably metacompact or not.