Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Riedel, Thomas

Committee Member

Powers, Robert

Committee Member

Sahoo, Prasanna

Committee Member

Peters, Susan A.

Author's Keywords

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.