Opérations de Hausdorff itérées et réunions croissantes de compacts
Kahane, Sylvain
Fundamenta Mathematicae, Tome 141 (1992), p. 169-194 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:211959 
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     author = {Sylvain Kahane},
     title = {Op\'erations de Hausdorff it\'er\'ees et r\'eunions croissantes de compacts},
     journal = {Fundamenta Mathematicae},
     volume = {141},
     year = {1992},
     pages = {169-194},
     zbl = {0763.04002},
     language = {fra},
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Kahane, Sylvain. Opérations de Hausdorff itérées et réunions croissantes de compacts. Fundamenta Mathematicae, Tome 141 (1992) pp. 169-194. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv141i2p169bwm/

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