Geodesic
On character of points in the Higson corona of a metric space
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 2, pp. 159-178.

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

We prove that for an unbounded metric space $X$, the minimal character $\mathsf m\chi(\check X)$ of a point of the Higson corona $\check X$ of $X$ is equal to $\mathfrak u$ if $X$ has asymptotically isolated balls and to $\max\{\mathfrak u,\mathfrak d\}$ otherwise. This implies that under $\mathfrak u \mathfrak d$ a metric space $X$ of bounded geometry is coarsely equivalent to the Cantor macro-cube $2^{\mathbb N}$ if and only if $\dim (\check X)=0$ and $\mathsf m\chi (\check X)= \mathfrak d$. This contrasts with a result of Protasov saying that under CH the coronas of any two asymptotically zero-dimensional unbounded metric separable spaces are homeomorphic.
Classification : 03E17, 03E35, 03E50, 54D35, 54E35, 54F45
Keywords: Higson corona; character of a point; ultrafilter number; dominating number 
@article{CMUC_2013__54_2_a3,
     author = {Banakh, Taras and Chervak, Ostap and Zdomskyy, Lubomyr},
     title = {On character of points in the {Higson} corona of a metric space},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {159--178},
     publisher = {mathdoc},
     volume = {54},
     number = {2},
     year = {2013},
     mrnumber = {3067701},
     zbl = {06221260},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2013__54_2_a3/}
}
TY  - JOUR
AU  - Banakh, Taras
AU  - Chervak, Ostap
AU  - Zdomskyy, Lubomyr
TI  - On character of points in the Higson corona of a metric space
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2013
SP  - 159
EP  - 178
VL  - 54
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2013__54_2_a3/
LA  - en
ID  - CMUC_2013__54_2_a3
ER  - 
%0 Journal Article
%A Banakh, Taras
%A Chervak, Ostap
%A Zdomskyy, Lubomyr
%T On character of points in the Higson corona of a metric space
%J Commentationes Mathematicae Universitatis Carolinae
%D 2013
%P 159-178
%V 54
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2013__54_2_a3/
%G en
%F CMUC_2013__54_2_a3
Banakh, Taras; Chervak, Ostap; Zdomskyy, Lubomyr. On character of points in the Higson corona of a metric space. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 2, pp. 159-178. http://geodesic.mathdoc.fr/item/CMUC_2013__54_2_a3/