## Electronic Theses and Dissertations

8-2017

#### Document Type

Doctoral Dissertation

Ph. D.

Mathematics

#### Degree Program

Applied and Industrial Mathematics, PhD

Riedel, Thomas

Powers, Robert

Powers, Robert

Sahoo, Prasanna

Peters, Susan A.

#### Author's Keywords

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

#### Abstract

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.

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