On Product of Metacompact Spaces

A topological space X is said to be paracompact if every open cover has a locally finite open refinement. A topological space in which every open cover admits a point-finite open refinement is called metacompact. If X is a paracompact P-space and Y is a Lindelöf space, then X × Y is paracompact. We answer an open problem and extend the latter statement for metacompact spaces instead of paracompact spaces, i.e., if X is a metacompact P-space and Y is a Lindelöf .space, then X × Y is metacompact