The Intrinsic Topologies of Partially Ordered Sets - Tong, Maoting; Ton, Daoron (European Journal of Applied Sciences, 2025)
In this article, we discuss the relationship and equivalence between the intrinsic topologies of a partially ordered set. The main results are Theorem 1-Theorem 9. The interval topology is coarser than the open interval topology in a partially ordered set. The order topology is coarser than the open interval topology in a lattice. In a partially ordered set P with finite divergence, L i= if and only if the limit of each L topological convergemt net in P is midpoint.