Countable metacompactness of products of LOTS'
A topological space \(X\) is said to be countably metacompact if each countable open cover has a point-finite open refinement. It is known that each LOTS and the product of two ordinals is hereditarily countably metacompact. For every regular uncountable cardinal \(\kappa,\) the authors construct a hereditarily paracompact LOTS \(L_\kappa\) such that \(L_\kappa\times S\) is not countably metacompact for any stationary set \(S\) in \(\kappa.\) They also find a condition on a GO-space \(X\) in order that \(X\times \kappa\) is countably metacompact. They conclude that a subspace \(X\) of an ordinal is paracompact if and only if \(X\times Y\) is countably metacompact for every GO-space \(Y.\)
scientific article; zbMATH DE number 6369776