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Irreducible convergence in \(T_0\) spaces. (English) Zbl 07201570
Summary: In this paper, we define and study irreducible convergence and irreducible order-convergence in \(T_0\) spaces, which can be seen as topological counterparts of lim-inf-convergence and order-convergence in posets, respectively. Especially, we give sufficient and necessary conditions for irreducible convergence and irreducible order-convergence in \(T_0\) spaces to be topological.

MSC:
06B30 Topological lattices
06B35 Continuous lattices and posets, applications
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
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