Morita Conjectures

The Morita conjectures in general topology are certain problems about normal spaces, now solved in the affirmative. They asked

  1. If X × Y is normal for every normal space Y, is X discrete?
  2. If X × Y is normal for every normal P-space Y, is X metrizable ?
  3. If X × Y is normal for every normal countably paracompact space Y, is X metrizable and sigma-locally compact?

Here a normal P-space Y is characterised by the property that the product with every metrizable X is normal; thus the conjecture was that the converse holds.

K. Chiba, T.C. Przymusiński and M.E. Rudin proved conjecture (1) and showed that conjecture (2) is true if the axiom of constructibility V=L, holds.

Z. Balogh proved conjectures (2) and (3).

Famous quotes containing the word conjectures:

    “After all, it is putting a very high price on one’s conjectures to have a man roasted alive because of them.”
    —Michel de Montaigne (1533–1592)