Pseudocomplete and weakly pseudocompact spaces

We prove that if X is a quasiregular, countably compact space with a pseudobase consisting of closed G δ -sets, then every G δ -dense subspace of X is pseudocomplete in the sense of Todd. In particular, every weakly pseudocompact space is pseudocomplete in the sense of Todd. Some sufficient conditions are found that guarantee that a weakly pseudocompact space is pseudocomplete in the sense of Oxtoby. It is shown that every weakly pseudocompact space without isolated points has cardinality at least continuum. An example is given of a weakly pseudocompact space with one non-isolated point that contains the one-point lindelöfication of an uncountable discrete space. We apply this example to show that weak pseudocompactness is not preserved by the relation of M-equivalence.