Geodesic
Universal meager $F_\sigma$-sets in locally compact manifolds
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 2, pp. 179-188 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In each manifold $M$ modeled on a finite or infinite dimensional cube $[0,1]^n$, $n\leq \omega $, we construct a meager $F_\sigma$-subset $X\subset M$ which is universal meager in the sense that for each meager subset $A\subset M$ there is a homeomorphism $h:M\to M$ such that $h(A)\subset X$. We also prove that any two universal meager $F_\sigma$-sets in $M$ are ambiently homeomorphic.
In each manifold $M$ modeled on a finite or infinite dimensional cube $[0,1]^n$, $n\leq \omega $, we construct a meager $F_\sigma$-subset $X\subset M$ which is universal meager in the sense that for each meager subset $A\subset M$ there is a homeomorphism $h:M\to M$ such that $h(A)\subset X$. We also prove that any two universal meager $F_\sigma$-sets in $M$ are ambiently homeomorphic.
Classification : 54F65, 57N20, 57N45
Keywords: universal nowhere dense subset; Sierpiński carpet; Menger cube; Hilbert cube manifold; $n$-manifold; tame ball; tame decomposition 
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     author = {Banakh, Taras and Repov\v{s}, Du\v{s}an},
     title = {Universal meager $F_\sigma$-sets in locally compact manifolds},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {179--188},
     year = {2013},
     volume = {54},
     number = {2},
     mrnumber = {3067702},
     zbl = {06221261},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2013_54_2_a4/}
}
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Banakh, Taras; Repovš, Dušan. Universal meager $F_\sigma$-sets in locally compact manifolds. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 2, pp. 179-188. http://geodesic.mathdoc.fr/item/CMUC_2013_54_2_a4/