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On topological spaces that have a bounded complete DCPO model
Citation
Zhao, D., & Xi, X. (2018). On topological spaces that have a bounded complete DCPO model. Rocky Mountain Journal of Mathematics, 48(1), 141-156. https://projecteuclid.org/euclid.rmjm/1524880885
Abstract
A dcpo model of a topological space X is a dcpo (directed complete poset) P such that X is homeomorphic to the maximal point space of P with the subspace topology of the Scott space of P. It has been proved previously by X. Xi and D. Zhao that every T1 space has a dcpo model. It is, however, still unknown whether every T1 space has a bounded complete dcpo model (a poset is bounded complete if each of its upper bounded subsets has a supremum). In this paper we rst show that the set of natural numbers equipped with the co- nite topology does not have a bounded complete dcpo model, then prove that a large class of topological spaces (including all Hausdorff k-spaces) have a bounded complete dcpo model. We shall mainly focus on the model formed by all the nonempty closed compact subsets of the given space.
Date Issued
2018
Publisher
Rocky Mountain Mathematics Consortium
Journal
Rocky Mountain Journal of Mathematics