Some results on [n,m]‐paracompact and [n,m]‐compact spaces

Let n and m be infinite cardinals with n ≤ 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, ∞]‐compact and Y be a [n, m]‐paracompact (resp. [n, ∞]‐paracompact), Pn‐space (resp. wPn‐space). If we prove that X × Y is [n, m]‐paracompact (resp. [n, ∞]‐paracompact