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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:
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.)


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