| Title:
|
When ${\rm Min}(G)^{-1}$ has a clopen $\pi $-base (English) |
| Author:
|
Lafuente-Rodriguez, Ramiro |
| Author:
|
McGovern, Warren Wm. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
146 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
69-89 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is our aim to contribute to the flourishing collection of knowledge centered on the space of minimal prime subgroups of a given lattice-ordered group. Specifically, we are interested in the inverse topology. In general, this space is compact and $T_1$, but need not be Hausdorff. In 2006, W. Wm. McGovern showed that this space is a boolean space (i.e. a compact zero-dimensional and Hausdorff space) if and only if the $l$-group in question is weakly complemented. A slightly weaker topological property than having a base of clopen subsets is having a clopen $\pi $-base. Recall that a $\pi $-base is a collection of nonempty open subsets such that every nonempty open subset of the space contains a member of the $\pi $-base; obviously, a base is a $\pi $-base. In what follows we classify when the inverse topology on the space of prime subgroups has a clopen $\pi $-base. (English) |
| Keyword:
|
lattice-ordered group |
| Keyword:
|
minimal prime subgroup |
| Keyword:
|
maximal $d$-subgroup |
| Keyword:
|
archimedean $l$-group |
| Keyword:
|
$\bold {W}$ |
| MSC:
|
06F15 |
| MSC:
|
06F20 |
| idZBL:
|
07332743 |
| idMR:
|
MR4227312 |
| DOI:
|
10.21136/MB.2020.0114-18 |
| . |
| Date available:
|
2021-03-12T16:20:08Z |
| Last updated:
|
2021-04-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148748 |
| . |
| Reference:
|
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