dc.contributor.advisor Tymchatyn, Edward dc.creator Assaf, Samer dc.date.accessioned 2016-07-18T20:42:48Z dc.date.available 2016-07-18T20:42:48Z dc.date.created 2016-06 dc.date.issued 2016-07-11 dc.date.submitted June 2016 dc.identifier.uri http://hdl.handle.net/10388/7351 dc.description.abstract A distance on a set is a comparative function. The smaller the distance between two elements of that set, the closer, or more similar, those elements are. Fr\'echet axiomatized the notion of distance into what is today known as a metric. In this thesis we study several generalizations of Fr\'echet's axioms. These include partial metric, strong partial metric, partial \$n-\mathfrak{M}\$etric and strong partial \$n-\mathfrak{M}\$etric. Those generalizations allow for negative distances, non-zero distances between a point and itself and even the comparison of \$n-\$tuples. We then present the scoring of a DNA sequence, a comparative function that is not a metric but can be modeled as a strong partial metric. \\\indent Using the generalized metrics mentioned above we create topological spaces and investigate convergence, limits and continuity in them. As an application, we discuss contractiveness in the language of our generalized metrics and present Banach-like fixed, common fixed and coincidence point theorems. dc.format.mimetype application/pdf dc.subject Partial metric dc.subject n-Metric dc.title Generalized Metrics dc.type Thesis dc.date.updated 2016-07-18T20:42:49Z thesis.degree.department Mathematics and Statistics thesis.degree.discipline Mathematics thesis.degree.grantor University of Saskatchewan thesis.degree.level Doctoral thesis.degree.name Doctor of Philosophy (Ph.D.) dc.type.material text dc.contributor.committeeMember Srinivasan, Raj dc.contributor.committeeMember Szmigielski , Jacek dc.contributor.committeeMember Martin, John dc.contributor.committeeMember Dutchyn, Christopher
﻿