Residuated maps, the way-below relation, and contractions on probabilistic metric spaces.

lattices;order;residuated maps;poset;way-below

M. Ryan Luke

University:University of Louisville

Department:Mathematics

关键词: lattices;    order;    residuated maps;    poset;    way-below;   

Others  :  https://ir.library.louisville.edu/cgi/viewcontent.cgi?article=3936&context=etd

美国|英语

来源: The Universite of Louisville's Institutional Repository

【 摘 要 】

In this dissertation, we will examine residuated mappings on a function lattice and how they behave with respect to the way-below relation. In particular, which residuated $\phi$ has the property that $F$ is way-below $\phi(F)$ for $F$ in appropriate sets. We show the way-below relation describes the separation of two functions and how this corresponds to contraction mappings on probabilistic metric spaces. A new definition for contractions is considered using the way-below relation.