Convex and Weakly Convex Subsets of a Pseudo Ordered Set


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Authors

  • Prashantha Rao Department of Mathematics, Sahyadri College of Engineering and Management, Adyar, Mangalore, Karnataka, India
  • Shashirekha B Rai Department of Mathematics, NMAMIT Nitte, Karkal, Karnataka, India

Keywords:

Psoset, convex subset, w-convex subset, w-convex hull, lattice

Abstract

In this paper the notion of convex and weakly convex (w-convex) subsets of a pseudo ordered set is introduced and several characterizations are proved. It is proved that set of all convex subsets of a pseudo ordered set $A$ forms a complete lattice. Notion of isomorphism of psosets is introduced and characterization for convex isomorphic psosets is obtained. It is proved that lattice of all w-convex subsets of a pseudo ordered set $A$ denoted by $WCS(A)$ is lower semi modular. Also we have proved that for any two pseudo ordered sets $A$ and $A^1$, w-convex homomorphism maps atoms of $WCS(A)$ to atoms of $WCS(A^1)$. Concept of path preserving mapping is introduced in a pseudo ordered set and it is proved that every mapping of a pseudo ordered set $A$ to itself is path preserving if and only if $A$ is a cycle.

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Published

15-03-2019

How to Cite

Prashantha Rao, & Shashirekha B Rai. (2019). Convex and Weakly Convex Subsets of a Pseudo Ordered Set. International Journal of Mathematics And Its Applications, 7(1), 149–154. Retrieved from https://ijmaa.in/index.php/ijmaa/article/view/276

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Section

Research Article