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

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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 
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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/