This analysis examines intrinsic topologies in partially ordered sets, revealing key equivalences.
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.
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Tong et al. (2025) studied this question.
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