Document Type : Primary Research paper
Nehru Institute of Technology, Coimbatore, Tamilnadu,India.
Inthispaperthenotionofconvexandweaklyconvex(w-convex)subsetsofapseudoorderedsetisintroducedandseveralcharacterizations are proved.It is proved that set of all convex subsets of a pseudo ordered set A forms a completelattice. 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 A1, w-convex homomorphism maps atoms of WCS(A)to atoms of WCS(A1). Concept of path preserving mapping is introduced in a pseudo ordered set and it is proved thateverymappingofapseudoorderedsetAtoitselfispathpreservingifandonlyifAisacycle