| Title:
|
On iterated limits of subsets of a convergence $\ell $-group (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
53-61 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we deal with the relation \[ \lim _\alpha \lim _\alpha X=\lim _\alpha X \] for a subset $X$ of $G$, where $G$ is an $\ell $-group and $\alpha $ is a sequential convergence on $G$. (English) |
| Keyword:
|
convergence $\ell $-group |
| Keyword:
|
disjoint subset |
| Keyword:
|
direct product |
| Keyword:
|
lexico extension |
| Keyword:
|
sequential convergence |
| MSC:
|
06F15 |
| MSC:
|
22C05 |
| idZBL:
|
Zbl 0978.06008 |
| idMR:
|
MR1826470 |
| DOI:
|
10.21136/MB.2001.133921 |
| . |
| Date available:
|
2009-09-24T21:47:11Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133921 |
| . |
| Reference:
|
[1] P. Conrad: The structure of a lattice ordered group with a finite number of disjoint elements.Michigan Math. J. 7 (1960), 171–180. Zbl 0103.01501, MR 0116059, 10.1307/mmj/1028998387 |
| Reference:
|
[2] P. Conrad: Lattice Ordered Groups.Lecture Notes, Tulane University, 1970. Zbl 0258.06011 |
| Reference:
|
[3] J. Jakubík: Direct decompositions of partially ordered groups, II.Czechoslovak Math. J. 11 (1961), 490–515. (Russian) MR 0137776 |
| Reference:
|
[4] J. Jakubík: Sequential convergences in $\ell $-groups without Urysohn’s axiom.Czechoslovak Math. J. 42 (1992), 101–116. MR 1152174 |
| Reference:
|
[5] J. Jakubík: Closed convex $\ell $-subgroups and radical classes of convergence $\ell $-groups.Math. Bohem. 122 (1997), 301–315. MR 1600660 |
| Reference:
|
[6] V. M. Kopytov, N. Ya. Medvedev: The Theory of Lattice Ordered Groups.Kluwer Academic Publishers, Dordrecht-Boston-London, 1994. MR 1369091 |
| . |
