Translator Disclaimer
2018 On topological spaces that have a bounded complete DCPO model
Zhao Dongsheng, Xi Xiaoyong
Rocky Mountain J. Math. 48(1): 141-156 (2018). DOI: 10.1216/RMJ-2018-48-1-141

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 previously proved by Xi and Zhao that every $T_1$ space has a dcpo model. It is, however, still unknown whether every $T_1$ 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 first show that the set of natural numbers equipped with the co-finite topology does not have a bounded complete dcpo model and 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 of the nonempty closed compact subsets of the given space.

Citation

Download Citation

Zhao Dongsheng. Xi Xiaoyong. "On topological spaces that have a bounded complete DCPO model." Rocky Mountain J. Math. 48 (1) 141 - 156, 2018. https://doi.org/10.1216/RMJ-2018-48-1-141

Information

Published: 2018
First available in Project Euclid: 28 April 2018

zbMATH: 06866704
MathSciNet: MR3795737
Digital Object Identifier: 10.1216/RMJ-2018-48-1-141

Subjects:
Primary: 06B30, 06B35, 54A05

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
16 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.48 • No. 1 • 2018
Back to Top