Partially ordered groups with two disjoint elements
J. Jakubík (1970)
Colloquium Mathematicae
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J. Jakubík (1970)
Colloquium Mathematicae
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Ján Jakubík (1990)
Czechoslovak Mathematical Journal
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Štefan Černák (1995)
Mathematica Slovaca
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Ján Jakubík (1989)
Archivum Mathematicum
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Bupurao C. Dhage (2006)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper, some algebraic fixed point theorems for multi-valued discontinuous operators on ordered spaces are proved. These theorems improve the earlier fixed point theorems of Dhage (1988, 1991) Dhage and Regan (2002) and Heikkilä and Hu (1993) under weaker conditions. The main fixed point theorems are applied to the first order discontinuous differential inclusions for proving the existence of the solutions under certain monotonicity condition of multi-functions.
Jiří Rachůnek (2000)
Mathematica Slovaca
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Dale Rolfsen (2014)
Banach Center Publications
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In this expository article we use topological ideas, notably compactness, to establish certain basic properties of orderable groups. Many of the properties we shall discuss are well-known, but I believe some of the proofs are new. These will be used, in turn, to prove some orderability results, including the left-orderability of the group of PL homeomorphisms of a surface with boundary, which are fixed on at least one boundary component.
Štefan Černák (2002)
Discussiones Mathematicae - General Algebra and Applications
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The notion of a half lc-group G is a generalization of the notion of a half linearly ordered group. A completion of G by means of Dedekind cuts in linearly ordered sets and applying Świerczkowski's representation theorem of lc-groups is constructed and studied.