View source for Morita conjectures

{{TEX|done}}{{MSC|54D}}

Three conjectures in [[general topology]]  due to K. Morita:

# If $X \times Y$ is [[normal space|normal]] for every normal space $Y$, is $X$ [[discrete space|discrete]]?
# If $X \times Y$ is normal for every normal [[P-space]] $Y$, is $X$ [[Metrizable space|metrizable]]?
# If $X \times Y$ is normal for every normal countably [[Paracompact space|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; it is thus conjectured 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 conjecture (3).

==References==
* K. Morita,   "Some problems on normality of products of spaces"  J. Novák (ed.) , Proc. Fourth Prague Topological Symp. (Prague, August 1976) , Soc. Czech. Math. and Physicists , Prague  (1977)  pp. 296–297
* A.V. Arhangelskii, K.R. Goodearl, B. Huisgen-Zimmermann, ''Kiiti Morita 1915-1995'', Notices of the AMS, June 1997 [http://www.ams.org/notices/199706/morita.pdf]
* K. Chiba,   T.C. Przymusiński,   M.E. Rudin,   "Normality of products and Morita's conjectures"  ''Topol. Appl.'' '''22'''  (1986)  19–32
* Z. Balogh, Non-shrinking open covers and K. Morita's duality conjectures, ''Topology Appl.'', '''115''' (2001) 333-341