Nehru Institute of Technology, Coimbatore, Tamilnadu,India.
Abstract
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
Maybell, S., Abinaya, A., S, K., & V, S. (2021). Convex and Weakly Convex Subsets of a Pseudo Ordered Set. Int. J. of Aquatic Science, 12(3), 655-661.
MLA
Sheeba Maybell; A. Abinaya; Karthik S; Shinduja, V. "Convex and Weakly Convex Subsets of a Pseudo Ordered Set". Int. J. of Aquatic Science, 12, 3, 2021, 655-661.
HARVARD
Maybell, S., Abinaya, A., S, K., V, S. (2021). 'Convex and Weakly Convex Subsets of a Pseudo Ordered Set', Int. J. of Aquatic Science, 12(3), pp. 655-661.
VANCOUVER
Maybell, S., Abinaya, A., S, K., V, S. Convex and Weakly Convex Subsets of a Pseudo Ordered Set. Int. J. of Aquatic Science, 2021; 12(3): 655-661.
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