ČERNÁK, Š.— JAKUBÍK, J.: Completion of a cyclically ordered group, Czechoslovak Math. J. 37 (1987), 157–174.
 FRIČ, R.— KOUTNÍK, V.: Recent development in sequential convergence. In: Convergence Structures and Applications II. Abh. Akad. Wiss. DDR, Abt. Math.-Naturwiss.-Technik, Akademie Verlag, Berlin, 1984, pp. 37–46.
 FUCHS, L.: Partially Ordered Algebraic Systems, Pergamon Press, Oxford-London-New York-Paris, 1963.
 HARMINC, M.: Sequential convergences on cyclically ordered groups. Math. Slovaca 38 (1988), 249–253. [Web of Science]
 HARMINC, M.: Sequential convergences on lattice ordered groups, Czechoslovak Math. J. 39 (1989), 232–238.
 JAKUBÍK, J.: Retracts of abelian cyclically ordered groups, Arch. Math. (Brno) 25 (1989), 13–18.
 JAKUBÍK, J.: Lattice ordered groups having a largest convergence, Czechoslovak Math. J. 39 (1989), 717–729.
 JAKUBÍK, J.: Sequential convergences in ℓ-groups without Urysohn’s axiom, Czechoslovak Math. J. 42 (1992), 101–116. [Web of Science]
 JAKUBÍK, J.: Lexicographic product decompositions of cyclically ordered groups, Czechoslovak Math. J. 48 (1998), 229–241. http://dx.doi.org/10.1023/A:1022881202595 [CrossRef]
 JAKUBÍK, J.— PRINGEROVÁ, G.: Representation of cyclically ordered groups, Časopis Pěst. Mat. 113 (1988), 197–208.
 JAKUBÍK, J.— PRINGEROVÁ, G.: Radical classes of cyclically ordered groups, Math. Slovaca 38 (1988), 255–268. [Web of Science]
 JAKUBÍK, J.— PRINGEROVÁ, G.: Direct limits of cyclically ordered groups, Czechoslovak Math. J. 44 (1994), 231–250.
 RIEGER, L.: On ordered and cyclically ordered groups, I; II; III, Věstník Král. České Spol. Nauk (1946); (1947); (1948), 1–31; 1–33; 1–26 (Czech).
 SWIERCZKOWSKI, S.: On cyclically ordered groups, Fund. Math. 47 (1959), 161–166.
 ZABARINA, A. I.: To the theory of cyclically ordered groups, Mat. Zametki 31 (1982), 3–12 (Russian).
 ZABARINA, A. I.— PESTOV, G. G.: To the Swierczkowski’s Theorem, Sibirsk. Mat. Zh. 25 (1984), 46–53 (Russian).
Volume 64 (2014)
Volume 63 (2013)
Volume 62 (2012)
Volume 61 (2011)
Volume 60 (2010)
Volume 59 (2009)
Volume 58 (2008)
Most Downloaded Articles
- Bases of measurability in Boolean algebras by Repický, Miroslav
- Henstock-Kurzweil-Pettis integral and weak topologies in nonlinear integral equations on time scales by Satco, Bianca-Renata and Turcu, Corneliu-Octavian
- On ΛIs-sets and the related notions in ideal topological spaces by Sanabria, José/ Rosas, Ennis and Carpintero, Carlos
- Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces by Aghajani, Asadollah/ Abbas, Mujahid and Roshan, Jamal
- Some properties of hyperideals in ternary semihypergroups by Naka, Krisanthi and Hila, Kostaq
Sequential convergences on cyclically ordered groups without Urysohn’s axiom
1Slovak Academy of Sciences
© 2008 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)
Citation Information: Mathematica Slovaca. Volume 58, Issue 6, Pages 739–754, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: 10.2478/s12175-008-0105-0, November 2008
- Published Online:
In this paper we investigate sequential convergences on a cyclically ordered group G which are compatible with the group operation and with the relation of cyclic order; we do not assume the validity of the Urysohn’s axiom. The system convG of convergences under consideration is partially ordered by means of the set-theoretical inclusion. We prove that convG is a Brouwerian lattice.
MSC: Primary 06F15