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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A proof of Nogura's conjecture


Author: Stevo Todorcevic
Journal: Proc. Amer. Math. Soc. 131 (2003), 3919-3923
MSC (2000): Primary 03E65, 54B10, 54D55
Published electronically: May 28, 2003
MathSciNet review: 1999941
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Abstract: Answering a question of T. Nogura (1985), we show using the Open Coloring Axiom that the weak diagonal sequence property is preserved by taking products whenever the products themselves are Fréchet. As an application we show, using the same assumption, that the product of two Fréchet groups is Fréchet provided it is sequential. Recall that the product of two Fréchet groups may not be sequential.


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Additional Information

Stevo Todorcevic
Affiliation: Université Paris 7 - C.N.R.S., UMR 7056, 2, Place Jussieu, 75251 Paris Cedex 05, France
Email: stevo@math.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07002-3
PII: S 0002-9939(03)07002-3
Keywords: Fr\'echet space, diagonal sequence property
Received by editor(s): August 1, 2002
Received by editor(s) in revised form: August 6, 2002
Published electronically: May 28, 2003
Communicated by: Alan Dow
Article copyright: © Copyright 2003 American Mathematical Society