The Morita conjectures in general topology are certain problems about normal spaces, now solved in the affirmative. The conjectures, formulated by Kiiti Morita in 1976, asked
If is normal for every normal space Y, is X a discrete space?
The answers were believed to be affirmative. Here a normal P-spaceY is characterised by the property that the product with every metrizable X is normal; thus the conjecture was that the converse holds.
Keiko Chiba, Teodor C. Przymusiński, and Mary Ellen Rudin[2] proved conjecture (1) and showed that conjectures (2) and (3) cannot be proven false under the standard ZFC axioms for mathematics (specifically, that the conjectures hold under the axiom of constructibilityV=L).
Fifteen years later, Zoltán Tibor Balogh succeeded in showing that conjectures (2) and (3) are true.[3]
^Morita, Kiiti (1977). "Some problems on normality of products of spaces". In Novák, Josef (ed.). General topology and its relations to modern analysis and algebra, IV (Proc. Fourth Prague Topological Sympos., Prague, 1976), Part B. Prague: Soc. Czechoslovak Mathematicians and Physicists. pp. 296–297. MR0482657.