Geodesic
Universal meager $F_\sigma$-sets in locally compact manifolds
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 2, pp. 179-188.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{CMUC_2013__54_2_a4,
     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},
     publisher = {mathdoc},
     volume = {54},
     number = {2},
     year = {2013},
     mrnumber = {3067702},
     zbl = {06221261},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2013__54_2_a4/}
}
TY  - JOUR
AU  - Banakh, Taras
AU  - Repovš, Dušan
TI  - Universal meager $F_\sigma$-sets in locally compact manifolds
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2013
SP  - 179
EP  - 188
VL  - 54
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2013__54_2_a4/
LA  - en
ID  - CMUC_2013__54_2_a4
ER  - 
%0 Journal Article
%A Banakh, Taras
%A Repovš, Dušan
%T Universal meager $F_\sigma$-sets in locally compact manifolds
%J Commentationes Mathematicae Universitatis Carolinae
%D 2013
%P 179-188
%V 54
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2013__54_2_a4/
%G en
%F CMUC_2013__54_2_a4
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/