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A construction of free dcpo-cones

Published online by Cambridge University Press:  10 January 2024

Yuxu Chen ,
Hui Kou ,
Zhenchao Lyu Open the ORCID record for Zhenchao Lyu [Opens in a new window]  and
Xiaolin Xie
Yuxu Chen
Affiliation:
School of Mathematics, Sichuan University, Chengdu, P. R. China
Hui Kou
Affiliation:
School of Mathematics, Sichuan University, Chengdu, P. R. China
Zhenchao Lyu*
Affiliation:
School of Mathematics, Sichuan University, Chengdu, P. R. China
Xiaolin Xie
Affiliation:
School of Mathematics, Sichuan University, Chengdu, P. R. China
*
Corresponding author: Zhenchao Lyu; Email: zhenchaolyu@scu.edu.cn
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Abstract

We give a construction of the free dcpo-cone over any dcpo. There are two steps for getting this result. Firstly, we extend the notion of power domain to directed spaces which are equivalent to $T_0$ monotone-determined spaces introduced by Erné, and we construct the probabilistic powerspace of the monotone determined space, which is defined as a free monotone determined cone. Secondly, we take D-completion of the free monotone determined cone over the dcpo with its Scott topology. In addition, we show that generally the valuation power domain of any dcpo is not the free dcpo-cone.

Keywords

Topological conemonotone determined conecontinuous valuationpoint-continuousD-completiondcpo-cone
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 34 , Issue 1 , January 2024 , pp. 63 - 79
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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