Concerning Sets of the First Baire Category with Respect to Different Metrics
Maria Moszyńska ; Grzegorz Sójka
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010), p. 47-54 / Harvested from The Polish Digital Mathematics Library
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We prove that if ϱH and δ are the Hausdorff metric and the radial metric on the space ⁿ of star bodies in ℝ, with 0 in the kernel and with radial function positive and continuous, then a family ⊂ ⁿ that is meager with respect to ϱH need not be meager with respect to δ. Further, we show that both the family of fractal star bodies and its complement are dense in ⁿ with respect to δ.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:281228 
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     title = {Concerning Sets of the First Baire Category with Respect to Different Metrics},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
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     year = {2010},
     pages = {47-54},
     zbl = {1207.54039},
     language = {en},
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Maria Moszyńska; Grzegorz Sójka. Concerning Sets of the First Baire Category with Respect to Different Metrics. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) pp. 47-54. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba58-1-6/