Abstract
AbstractWe study a basic problem: in what posets is the order-convergence topological? We introduce the notion of 𝓡∗-doubly continuous posets, which extends the notion of doubly continuous posets, and then prove that the order-convergence in a poset is topological if and only if the poset is 𝓡∗-doubly continuous. This is the main result which can be regarded as a complete characterization of posets for the order-convergence being topological.
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