The product of two ordinals is hereditarily countably metacompact

It will be shown that μ × ν is hereditarily countably metacompact for any ordinals μ and ν. As an immediate corollary we see that ω12 is hereditarily countably metacompact. This answers a question of Ohta (K. Tamano, 1995). Also, as a corollary we see that if A and B are subspaces of ordinals, then A × B is countably metacompact. This corollary answers Question (iii) of N. Kemoto et al. (1992, p. 250).