Date on Master's Thesis/Doctoral Dissertation
Applied and Industrial Mathematics, PhD
Committee Co-Chair (if applicable)
Peters, Susan A.
lattices; order; residuated maps; poset; way-below
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.
Luke, M. Ryan, "Residuated maps, the way-below relation, and contractions on probabilistic metric spaces." (2017). Electronic Theses and Dissertations. Paper 2746.