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 Co-Chair (if applicable)

Powers, Robert

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.