On character of points in the Higson corona of a metric space

Banakh, Taras O., Chervak, Ostap, and Zdomskyy, Lubomyr. "On character of points in the Higson corona of a metric space." Commentationes Mathematicae Universitatis Carolinae 54.2 (2013): 159-178. <http://eudml.org/doc/252456>.

@article{Banakh2013,
abstract = {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 \lbrace \mathfrak \{u\},\mathfrak \{d\}\rbrace $ 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.},
author = {Banakh, Taras O., Chervak, Ostap, Zdomskyy, Lubomyr},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Higson corona; character of a point; ultrafilter number; dominating number; Higson corona; character of a point; ultrafilter number; dominating number},
language = {eng},
number = {2},
pages = {159-178},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On character of points in the Higson corona of a metric space},
url = {http://eudml.org/doc/252456},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Banakh, Taras O.
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
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 2
SP - 159
EP - 178
AB - 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 \lbrace \mathfrak {u},\mathfrak {d}\rbrace $ 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.
LA - eng
KW - Higson corona; character of a point; ultrafilter number; dominating number; Higson corona; character of a point; ultrafilter number; dominating number
UR - http://eudml.org/doc/252456
ER -