| Title:
|
On sequences in vector lattices (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
120 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
379-385 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate conditions for a system of sequences of elements of a vector lattice; analogous conditions for systems of sequences of reals were studied by D. E. Peek. (English) |
| Keyword:
|
vector lattice |
| Keyword:
|
$o$-convergence |
| Keyword:
|
Archimedean property |
| MSC:
|
40A05 |
| MSC:
|
46A40 |
| idZBL:
|
Zbl 0852.46005 |
| idMR:
|
MR1415085 |
| DOI:
|
10.21136/MB.1995.126094 |
| . |
| Date available:
|
2009-09-24T21:13:07Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126094 |
| . |
| Reference:
|
[1] G. Birkhoff: Lattice Theory.3rd ed.. Amer. Math. Soc. Colloquium Publications, Vol. 25, 1957. |
| Reference:
|
[2] R. Frič: On limits without epsilons.Real Analysis Exchange 19 (1993/94), 129-134. MR 1268838, 10.2307/44153821 |
| Reference:
|
[3] J. Jakubík: On the convergence in linear spaces.Matem. fyz. časopis 6 (1956), 57-67. (In Slovak.) MR 0084718 |
| Reference:
|
[4] J. Jakubík: On systems of sequences of reals.Tatra Mountains Math. Publ. 2, 1993, pp. 19-23. MR 1251033 |
| Reference:
|
[5] B. Kirchheim: The squeezing theorem is independent.Real Analysis Exchange 18 (1992/93), no. 2, 568-570. MR 1228426, 10.2307/44152305 |
| Reference:
|
[6] W. A. J. Luxemburg A. C. Zaanen: Riesz spaces, I..North Holland, Amsterdam, 1971. |
| Reference:
|
[7] D. E. Peek: Limits without epsilons.Real Analysis Exchange 17 (1991/92), 751-758. MR 1171415, 10.2307/44153767 |
| Reference:
|
[8] B. Z. Vulikh: Introduction to the theory of partially ordered spaces.Moskva, 1961. (In Russian.) |
| . |
