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Sums, products, and mappings of weakly pseudocompact spaces. (English) Zbl 0857.54022

Summary: Each 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) each summand is either weakly pseudocompact or locally compact Lindelöf and (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 \(G_\delta\)-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.

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54E52 Baire category, Baire spaces
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
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