Please use this identifier to cite or link to this item:
Zhao, D., Xi, X., & Chen, Y. (2020). Topologies generated by families of sets and strong poset models. Topology Proceedings, 56, 249-261.
A poset model of a topological space X is a poset P such that X is homeomorphic to the maximal point space of P (the set Max(P) of all maximal points of P equipped with the relative Scott topology of P). The poset models of topological spaces based on other topologies, such as Lawson topology and lower topology, have also been investigated by other people. These models establish various types of new links between posets and topological spaces. In this paper we introduce the strong Scott topology on a poset and use it to de ne the strong poset model: a strong poset model of a space X is a poset P such that Max(P) (equipped with the relative strong Scott topology) is homeomorphic to X. The main aim is to establish a characterization of T1 spaces with T-generated topologies (such as the Hausdor k-spaces) in terms of maximal point spaces of posets. A poset P is called ME-separated if for any elements x; y of P, x y i " y \ Max(P) "x \ Max(P). We consider the topological spaces that have an ME-separated strong poset model. The main result is that a T1 space has an ME-separated strong poset model i its topology is T-generated. The class of spaces whose topologies are T-generated include all Scott spaces and all Hausdor k-spaces.
This is the original draft, prior to peer-review, of a manuscript published in Topology Proceedings. The published version is available online at http://topology.auburn.edu/tp/reprints/v56/tp56015p1.pdf
NIE AcRF Project (Grant no. RI 3/16 ZDS)
NSF Project of Jiangsu Province, China (Grant no. BK20170483)
NSF of China (Grant no. 11361028)
NSF of China (Grant no. 61300153)
NSF of China (Grant no. 11671008)
NSF of China (Grant no. 11626207)
NSF of China (Grant no. 11701500)
NSF of China (Grant no. 61370100)
National Institute of Education (NIE), Singapore
|Appears in Collections:||Journal Articles|
Show full item record
Files in This Item:
|TP-56-249.pdf||368.79 kB||Adobe PDF|
Page view(s) 20250
checked on Jun 2, 2023
checked on Jun 2, 2023
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.