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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.

References [Enhancements On Off] (What's this?)

  • 1. R. Arens, Note on convergence in topology, Math. Magazine 23 (1950), 229-234. MR 12:271h
  • 2. T. Nogura, The product of $\langle \alpha_i\rangle-$spaces, Topology and its Appl. 21(1985), 251-259. MR 87d:54006
  • 3. P. Nyikos, Metrizability and the Fréchet-Urysohn property in topological groups, Proc. Amer. Math. Soc. 83 (1981), 793-801. MR 82k:54049
  • 4. D. Shakhmatov, Convergence in the presence of algebraic structure, in: Recent Progress in Topology (M. Husek and J. van Mill, eds.), to appear.
  • 5. A. Shibakov, Examples of sequential topological groups under the continuum hypothesis, Fund. Math. 151 (1996), 107-120. MR 97k:54021
  • 6. P. Simon, A hedgehog in a product, Acta Univ. Carolinae Math. Phys. 39 (1998), 147-153. MR 2000d:54033
  • 7. P. Simon and G. Tironi, No hedgehog in the product?, Comment. Math. Univ. Carolinae 43 (2002), 349-361.
  • 8. S. Todorcevic, Partition Problems in Topology, Contemp. Math., Vol. 84, American Math. Soc., Providence, RI, 1989. MR 90d:04001
  • 9. S. Todorcevic, Some applications of S and L combinatorics, Ann. New York Acad. Sci. 705(1993), 130-167. MR 95j:54006
  • 10. S. Todorcevic, Analytic Gaps, Fund. Math. 150(1996), 55-66. MR 98j:03070
  • 11. S. Todorcevic and C. Uzcategui Analytic k-spaces, preprint, 2000.

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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

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

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