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ArticleOriginal scientific text

Title

Opérations de Hausdorff itérées et réunions croissantes de compacts

Authors 1

Affiliations

  1. Equipe d'Analyse, Université Paris 6, 4, Place Jussieu, 75252 Paris Cedex 05, France

Abstract

In this paper, motivated by questions in Harmonic Analysis, we study the operation of (countable) increasing union, and show it is not idempotent: ω1 iterations are needed in general to obtain the closure of a class under this operation. Increasing union is a particular Hausdorff operation, and we present the combinatorial tools which allow to study the power of various Hausdorff operations, and of their iterates. Besides countable increasing union, we study in detail a related Hausdorff operation, which preserves compactness.

Bibliography

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm141/fm14125.pdf

Fundamenta Mathematicae
1992/141/2
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Pages:
169-194
Main language of publication
French
Received
1991-09-09
Accepted
1992-03-10
Published
1992
Exact and natural sciences