Order Convergence and Distance on Lukasiewicz-Moisil Algebras.
George Geordesce, Ioana Leuştean, Andrei Popescu · 2006
The paper develops a studyof order convergence in Łukasiewicz-Moisil algebras. An axiomatical notion of distance (covering the pointwise and the Heyting distances) is provided, together with an associated notion of Cauchysequence. Under natural hypotheses, it is proven the existence of Cauchycompletions. It is analy zed the connection to Boolean algebras along the canonical adjunction. The special class of proper LMm-algebras with Łukasiewicz distance is also investigated. Finally, we provide characterizations for the Cauchycompletions corresponding to some particular class of axiomatic distances.