Sums, products, and mappings of weakly pseudocompact spaces

AbstractEach open subspace of a weakly pseudocompact space is either weakly pseudocompact or locally compact Lindelöf. A topological sum is weakly pseudocompact if and only if 1.(1) each summand is either weakly pseudocompact or locally compact Lindelöf and2.(2) the sum is either compact or not Lindelöf. If X is realcompact and the lattice of compactifications of X is a b-lattice or if X is a not Čech-complete Gδ-diagonal space then X is not weakly pseudocompact. Weak pseudocompactness is neither an inverse invariant of perfect maps nor an invariant of open maps with compact fibers. There is a not pseudocompact space in which each zero set is weakly pseudocompact