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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

Publication History

Published Online:
2008-11-04

Abstract

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

Keywords: cyclically ordered group; sequential convergence; Brouwerian lattice

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