A proof of Nogura's conjecture

Author:
Stevo Todorcevic

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3919-3923

MSC (2000):
Primary 03E65, 54B10, 54D55

DOI:
https://doi.org/10.1090/S0002-9939-03-07002-3

Published electronically:
May 28, 2003

MathSciNet review:
1999941

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-03-07002-3

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