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 ^[1]?
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 ^[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]

Notes

1. ^ 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
2. ^ K. Chiba, T.C. Przymusiński, M.E. Rudin, "Normality of products and Morita's conjectures" Topol. Appl. 22 (1986) 19–32
3. ^ Z. Balogh, Non-shrinking open covers and K. Morita's duality conjectures, Topology Appl., 115 (2001) 333-341

References

• A.V. Arhangelskii, K.R. Goodearl, B. Huisgen-Zimmermann, Kiiti Morita 1915-1995, Notices of the AMS, June 1997 [1]

This topology-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Topology Conjectures Topology stubs Wikimedia Foundation. 2010. Игры ⚽ Поможем написать курсовую Small Town Girl (Good Shoes song) Parijnanashram III Look at other dictionaries: Morita (surname) — Morita a Japanese surname. Notable persons with that surname include: Akio Morita, co founder of the Sony Corporation Doji Morita, Japanese psych folk singer songwriter Hiroyuki Morita, Japanese animation director (The Cat Returns,...) Jungo… …   Wikipedia Kiiti Morita — (February 11, 1915, Hamamatsu ndash; August 4, 1995, Tokyo) 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.He introduced the… …   Wikipedia Zoltán Tibor Balogh — Zoltán Zoli Tibor Balogh (December 7, 1953 – June 19, 2002) was a Hungarian born mathematician, specializing in set theoretic topology. His father, Tibor Balogh, was also a mathematician.His best known results concerned solutions to problems… …   Wikipedia List of mathematics articles (M) — NOTOC M M estimator M group M matrix M separation M set M. C. Escher s legacy M. Riesz extension theorem M/M/1 model Maass wave form Mac Lane s planarity criterion Macaulay brackets Macbeath surface MacCormack method Macdonald polynomial Machin… …   Wikipedia Mary Ellen Rudin — (born December 7, 1924, Hillsboro, Texas) 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.[1] In 1953, she married the… …   Wikipedia Automate cellulaire — À gauche, une règle locale simple : une cellule passe d un état (i) au suivant (i+1) dans le cycle d états dès que i+1 est présent dans au moins 3 cellules voisines. À droite, le résultat (complexe) de l application répétée de cette règle… …   Wikipédia en Français Mapping class group — In mathematics, in the sub field of geometric topology, the mapping class group is an important algebraic invariant of a topological space. Briefly, the mapping class group is a discrete group of symmetries of the space. Contents 1 Motivation 2… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”