On order convergence
Pei Pei Ong · NIE Digital Repository (National Institute of Education, Nanyang Technological University) · 2003
For a given partially ordered set P one call define two convergences of sequences in P in terms of the order on P. One is the order-convergence another is the (t)- convergence. If {Xn) order-converges to T then it (t) - converges to X. But the converse implication is not always true. In this project we shall explore the relationship between these two convergences in different types of posets. We shall prove that for a completely distributive lattice L, the two convergences are equivalent. An example is provided to show that they are different in a poset of functions.