| Title:
|
On character of points in the Higson corona of a metric space (English) |
| Author:
|
Banakh, Taras |
| Author:
|
Chervak, Ostap |
| Author:
|
Zdomskyy, Lubomyr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
159-178 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Higson corona |
| Keyword:
|
character of a point |
| Keyword:
|
ultrafilter number |
| Keyword:
|
dominating number |
| MSC:
|
03E17 |
| MSC:
|
03E35 |
| MSC:
|
03E50 |
| MSC:
|
54D35 |
| MSC:
|
54E35 |
| MSC:
|
54F45 |
| idZBL:
|
Zbl 06221260 |
| idMR:
|
MR3067701 |
| . |
| Date available:
|
2013-06-25T12:47:56Z |
| Last updated:
|
2015-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143267 |
| . |
| Reference:
|
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