The Intrinsic Topologies of Partially Ordered Sets

Authors

  • Maoting Tong Public Basic Department, Nanjing Vocational University of Industry Technology, Nanjing, 210023, P.R.China
  • Daoron Ton Department of Mathematics, Hohai University, Nanjing, 210098, P.R.China

DOI:

https://doi.org/10.14738/aivp.1305.19428

Keywords:

Partially ordered set, Intrinsic topology, Sequential convergence, Finite divergence

Abstract

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.

Downloads

Published

2025-09-29

How to Cite

Tong, M., & Ton, D. (2025). The Intrinsic Topologies of Partially Ordered Sets . European Journal of Applied Sciences, 13(05), 210–219. https://doi.org/10.14738/aivp.1305.19428

Issue

Vol. 13 No. 05 (2025): European Journal of Applied Sciences

Section

Articles

License

Copyright (c) 2025 Maoting Tong, Daoron Ton

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.