Solutions of Separation, Simple Union and Simple Intersection Equations

Authors(2) :-Daniel Arficho Gaenore, Kindie Fentakun Muchie

Separation, simple union and simple intersection equations of sets are particular set equations with some special properties. The formal definition of separation, simple union and simple intersection equations of sets is given in introduction section. In this research, we study properties of solutions of separation, simple union and simple intersection equations of sets. We use some set operations and De Morgan’s law to investigate some facts of separation, simple union and simple intersection equations of sets. Further, we study the relation between separated sets and separation equation of sets. In addition, we investigate necessary and sufficient condition for solutions of separation equation.

Authors and Affiliations

Daniel Arficho Gaenore
Department of Mathematics, Wachamo University, Hossana, Ethiopia
Kindie Fentakun Muchie
Department of Epidemiology and Biostatistics, Bahir Dar University, Bahir Dar, Ethiopia

Disjoint, Operation, Separated Sets, Sigma algebra, Solution, Topology

  1. J. K. Hunter. Measure theory. University Lecture Notes, Department of Mathematics, University of California at Davis, 2011.
  2. G. S. Lo. Measure theory and integration by and for the learner. arXiv preprint arXiv:1711.04625, 2017.
  3. N. Bourbaki. General Topology. Chapters 1–4, volume 18. Springer Science and Business Media, 2013.
  4. K. P. Hart, J. -i. Nagata, and J. E. Vaughan. Encyclopedia of general topology. Elsevier, 2003.
  5. J. I. Nagata. Modern general topology. Elsevier, volume 33, 1985.\
  6. S. Willard. General topology. Courier Corporation, 2004.

Publication Details

Published in : Volume 2 | Issue 5 | September-October 2019
Date of Publication : 2019-10-30
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 16-20
Manuscript Number : GISRRJ19254
Publisher : Technoscience Academy

ISSN : 2582-0095

Cite This Article :

Daniel Arficho Gaenore, Kindie Fentakun Muchie, "Solutions of Separation, Simple Union and Simple Intersection Equations", Gyanshauryam, International Scientific Refereed Research Journal (GISRRJ), ISSN : 2582-0095, Volume 2, Issue 5, pp.16-20, September-October.2019
URL : https://gisrrj.com/GISRRJ19254

Article Preview