Date on Master's Thesis/Doctoral Dissertation
8-2017
Document Type
Doctoral Dissertation
Degree Name
Ph. D.
Department
Mathematics
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
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.
Recommended Citation
Luke, M. Ryan, "Residuated maps, the way-below relation, and contractions on probabilistic metric spaces." (2017). Electronic Theses and Dissertations. Paper 2746.
https://doi.org/10.18297/etd/2746
Included in
Algebra Commons, Analysis Commons, Other Mathematics Commons
