Please use this identifier to cite or link to this item:
http://hdl.handle.net/10497/15606
Title: | Authors: | Subjects: | Scott topology Sober space dcpo Dominated dcpo, H-continuous H-algebraic H-compact Strongly H-algebraic |
Issue Date: | 2010 |
Abstract: | A topological space is sober if every nonempty irreducible closed set is the closure of a unique singleton set. Sobriety is precisely the topological property that allows one to recover completely a topological space from its frame of opens. Because every Hausdor space is sober, sobriety is an overt, and hence unnamed, notion. Even in non-Hausdor settings, sober spaces abound. A well-known instance of a sober space appears in domain theory: the Scott topology of a continuous dcpo is sober. The converse is false as witnessed by two counterexamples constructed in the early 1980's: the first by P.T. Johnstone and the second (a complete lattice) by J. Isbell. Since then, there has been limited progress in the quest for an order-theoretic characterization of those dcpo's for which their Scott topology is sober. This paper provides one answer to this open problem. |
Description: | Technical report M2010-02, September 2010, Mathematics and Mathematics Education, National Institute of Education, Singapore |
URI: | File Permission: | Open |
File Availability: | With file |
Appears in Collections: | Research Reports |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
technicalreport_MME_a.pdf | 719.97 kB | Adobe PDF | View/Open |
Page view(s) 20
209
checked on Mar 17, 2023
Download(s) 50
143
checked on Mar 17, 2023
Google ScholarTM
Check
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.