Please use this identifier to cite or link to this item: http://hdl.handle.net/10497/21415
Title: 
Authors: 
Issue Date: 
2018
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.
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.
Description: 
This is the final draft, after peer-review, of a manuscript published in Rocky Mountain Journal of Mathematics. The published version is available online at https://projecteuclid.org/euclid.rmjm/1524880885
URI: 
ISSN: 
0035-7596
Website: 
Appears in Collections:Journal Articles

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