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.
In the paper an additive closure operator on an abelian unital -group is introduced and one studies the mutual relation of such operators and of additive closure ones on the -algebra .
In this paper it is proved that an abelian lattice ordered group which can be expressed as a nontrivial lexicographic product is never affine complete.
Let and be a nonzero abelian linearly ordered group or a nonzero abelian lattice ordered group, respectively. In this paper we prove that the wreath product of and fails to be affine complete.
In spite of increasing studies and investigations in the field of aggregation operators, there are two fundamental problems remaining unsolved: aggregation of -fuzzy set-theoretic notions and their justification. In order to solve these problems, we will formulate aggregation operators and their special types on partially ordered sets with universal bounds, and introduce their categories. Furthermore, we will show that there exists a strong connection between the category of aggregation operators...
A DC-space (or space of dense constancies) is a Tychonoff space such that for each there is a family of open sets , the union of which is dense in , such that , restricted to each , is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean -algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions...