Solution of Morita's problems concerning countably-compact-ifications

AbstractWe will prove that an M-space need not be countably-compact-ifiable. This implies that in the class of Tychonoff spaces, an M-space need not be homeomorphic to a closed subspace of the product of a countably compact space with a metric space. Further we construct, assuming the continuum hypothesis, a normal M-space which is not countably-compact-ifiable. It will also be shown that the product of two countably compact spaces is not necessarily countably-compact-ifiable