Valuations and their generalizations for UP-algebras
Siriwan Pawai, Tararat Khamsang, Aiyared Iampan · Open Journal of Mathematical Sciences · 2020
In this paper, we introduce the notions of a weak pseudo-valuation, a 0-weak pseudo-valuation, a weak valuation, a near pseudo-valuation, a near valuation, a pseudo-valuation, and a valuation and induce a pseudo-metric without triangle inequality, a quasi pseudo-metric, a pseudo-metric, and a metric by some these mappings on a UP-algebra.We also prove that the binary operation defined on a UP-algebra is uniformly continuous under the induced metric by a valuation in some conditions.