Morita conjectures: Difference between revisions
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The '''Morita conjectures''' in [[topology]] ask | The '''Morita conjectures''' in [[topology]] ask | ||
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==References== | ==References== | ||
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* 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] | * 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][[Category:Suggestion Bot Tag]] | ||
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Latest revision as of 11:00, 21 September 2024
The Morita conjectures in topology ask
- If X × Y is normal for every normal space Y, is X discrete?
- If X × Y is normal for every normal P-space Y, is X metrizable [1]?
- 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; it is thus conjectured that the converse holds.
K. Chiba, T.C. Przymusiński and M.E. Rudin [2] 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)[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
- ↑ 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
- A.V. Arhangelskii, K.R. Goodearl, B. Huisgen-Zimmermann, Kiiti Morita 1915-1995, Notices of the AMS, June 1997 [1]