Infinite-Dimensionality modulo Absolute Borel Classes

Vitalij Chatyrko; Yasunao Hattori

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008), p. 163-176 / Harvested from The Polish Digital Mathematics Library

Access to full text
Full (PDF)

Résumé

For each ordinal 1 ≤ α < ω₁ we present separable metrizable spaces $X_{α}$ , $Y_{α}$ and $Z_{α}$ such that (i) $f X_{α}, f Y_{α}, f Z_{α} = ω ₀$ , where f is either trdef or ₀-trsur, (ii) $A (α) - t r i n d X_{α} = \infty$ and $M (α) - t r i n d X_{α} = - 1$ , (iii) $A (α) - t r i n d Y_{α} = - 1$ and $M (α) - t r i n d Y_{α} = \infty$ , and (iv) $A (α) - t r i n d Z_{α} = M (α) - t r i n d Z_{α} = \infty$ and $A (α + 1) \cap M (α + 1) - t r i n d Z_{α} = - 1$ . We also show that there exists no separable metrizable space $W_{α}$ with $A (α) - t r i n d W_{α} \neq \infty$ , $M (α) - t r i n d W_{α} \neq \infty$ and $A (α) \cap M (α) - t r i n d W_{α} = \infty$ , where A(α) (resp. M(α)) is the absolutely additive (resp. multiplicative) Borel class.

Publié le : 2008-01-01

Zbl 1153.54016

EUDML-ID : urn:eudml:doc:281221

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-2-7,
     author = {Vitalij Chatyrko and Yasunao Hattori},
     title = {Infinite-Dimensionality modulo Absolute Borel Classes},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     volume = {56},
     year = {2008},
     pages = {163-176},
     zbl = {1153.54016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-2-7}
}

Vitalij Chatyrko; Yasunao Hattori. Infinite-Dimensionality modulo Absolute Borel Classes. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) pp. 163-176. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-2-7/