


  Axiomatic set theory 

  Axiomatic analysis via value quantales Author: Chand, Alveen Aditya Institution: University of the South Pacific. Award: M.Sc. Mathematics Subject: Lattice theory, Ordered algebraic structures, Axiomatic set theory Date: 2014 Call No.: Pac QA 171 .5 .C53 2014 BRN: 1197593 Copyright:2040% of this thesis may be copied without the authors written permission Abstract: Since the introduction of the notion of metric space, mathematics have shown immense interest towards it. Metric spaces represent an abstraction of the notion of distance, thus significant proportion of the research throughout the decades has been focused on its axioms. This thesis discusses a systematic analysis of quantale valued metric spaces (or V spaces), a generalization of metric spaces which uses value quantales. A comparative study of basic results in Metric Analysis is conducted in regards to value quantales. Some significant results such as continuity of the binary operations on Vspaces are established along with results on sequential continuity, convergence of monotone nets and a generalized Squeeze Lemma. Some of these results enlighten on the importance of the properties of real numbers and assist in categorizing the properties as either general or special . Also, an example of the value quantale of distance distribution function is presented in detail; such an example is harly shown in existing literature. Furthermore, a construction of the completion of Vspaces which satisfy uniformly vanishing asymmetry (a weak form of sysmmetry) is given using Cauchy filters. This construction along with other results on Vspaces establish that quantale valued metric spaces give a powerful axiomatization of Analysis.


