Some results on \([n,m]\)-paracompact and \([n,m]\)-compact spaces (Q1363184)

Summary: Let \(n\) and \(m\) be infinite cardinals with \(n\leq m\) and \(n\) be a regular cardinal. We prove certain implications of \([n,m]\)-strongly paracompact, \([n,m]\)-paracompact and \([n,m]\)-metacompact spaces. Let \(X\) be \([n,\infty]\)-compact and \(Y\) be a \([n,m]\)-paracompact (resp. \([n,\infty]\)-paracompact) \(P_n\)-space (resp. \(wP_n\)-space). If \(m= \sum_{k<n} m^k\) we prove that \(X\times Y\) is \([n,m]\)-paracompact (resp. \([n,\infty]\)-paracompact).