The Morita

Kiiti Morita

was a Japanese mathematician working in algebra and topology.He received his Ph.D. from the University of Osaka in 1950 and was professor at the University of Tsukuba....

 conjectures in general topology

General topology

In mathematics, general topology or point-set topology is the branch of topology which studies properties of topological spaces and structures defined on them...

 are certain problems about normal space

Normal space

In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have disjoint open neighborhoods. A normal Hausdorff space is also called a T4 space...

s, now solved in the affirmative. They asked

1. If X × Y is normal for every normal space Y, is X discrete
   Discrete space
   In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points are "isolated" from each other in a certain sense.- Definitions :Given a set X:...
   
   ?
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

Mary Ellen Rudin

Mary Ellen Rudin is an American mathematician.Born Mary Ellen Estill, she attended the University of Texas, completing her B.A. in 1944 and her Ph.D. in 1949, under Robert Lee Moore. In 1953, she married the mathematician Walter Rudin. Following her mentor Moore, her research centers on point-set...

proved conjecture (1) and showed that conjecture (2) is true if the axiom of constructibility

Axiom of constructibility

The axiom of constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible. The axiom is usually written as V = L, where V and L denote the von Neumann universe and the constructible universe, respectively.- Implications :The axiom of...

 V=L, holds.

Z. Balogh

Zoltán Tibor Balogh

Zoltán "Zoli" Tibor Balogh was a Hungarian-born mathematician, specializing in set-theoretic topology. His father, Tibor Balogh, was also a mathematician. His best known work concerned solutions to problems involving normality of products, most notably the first ZFC construction of a small ...

proved conjectures (2) and (3).