A proof of Nogura’s conjecture

Todorcevic, Stevo

doi:10.1090/S0002-9939-03-07002-3

A proof of Nogura’s conjecture
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Proc. Amer. Math. Soc. 131 (2003), 3919-3923 Request permission

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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