In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.

A topology on a lattice L or more generally on a partially ordered set P is called an intrinsic topology if it is de ned directly from the order Early ex amples of such topologies were the interval topology of O Frink Fr and the order topology introduced by G Birkho Bi The early intrinsic topolo gies were typically symmetric i e the topology de ned on L agreed with the topology de ned on L the ...

A partially ordered set (X, is called sharply transitive if its automorphism group is sharply transitive on X, that is, it is transitive and the stabilizer of every element is triviaL It is shown that every free group is the automorphism group of a sharply transitive partially ordered set. It is also shown that there exists a sharply transitive partially ordered set (-,Y, :::;) having some maxi...

Ralph Freese Department of Mathematics University of Hawaii at Manoa Honolulu, Hawaii 96822 In this paper we look at some of the problems on free lattices and free modular lattices which are of an order theoretic nature. We review some of the known results, give same new results, and present several open problems. Every countable partially ordered set can be order embedded into a countable free...

we report the direct soft chemical synthesis and characterization of a family of face centered cubic (fcc) and partially ordered face centered tetragonal (fct) fept nanoparticles (nps) suitable for biomedical applications. both fcc and partially ordered fct-fept nps are synthesized by employing a simple polyol method. by using polyvinyl pyrolidone (pvp) as a stabilizer in various ratios during ...