A note on the problem when FS-domains coincide with RB-domains

Document Type : Research Paper

Authors

1 College of Mathematics and Econometrics, Hunan University, Changsha, China

2 College of Mathematics and Computer Science, Hunan Normal University, Changsha, China

10.29252/cgasa.8.1.51

Abstract

In this paper, we introduce the notion of super finitely separating functions which gives a characterization of RB-domains. Then we prove that FS-domains and RB-domains are equivalent in some special cases by the following three claims: a dcpo is an RB-domain if and only if there exists an approximate identity for it consisting of super finitely separating functions; a consistent join-semilattice is an FS-domain if and only if it is an RB-domain; an L-domain is an FS-domain if and only if it is an RB-domain. These results are expected to provide useful hints to the open problem of whether FS-domains are identical with RB-domains.

Keywords

References

[1] Abramsky, S. and Jung, A., "Domain theory", Oxford University Press, Oxford,1994.
[2] Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M., and Scott, D.S., "Continuous Lattices and Domains", Encyclopedia of Mathematics and its Applications 93, Cambridge University Press, 2003.
[3] Heckmann R., "Characterising FS-domains by means of power domains", Theoret. Comput. Sci. 264(2) (2010), 195-203.
[4] Jung A., "Cartesian closed categories of domains", Ph.D. Thesis, FB Mathematik, Technische Hochschule Darmstadt, 1988.
[5] Jung A., "The classication of continuous domains", Logic in Computer Science LICS’ 90, IEEE Computer Society Press, Silver Spring, MD, 1990, 35-40.
[6] Lawson J.D., "Metric spaces and FS-domains", Theoret. Comput. Sci. 405(1-2) (2008), 73-74.
[7] Liang J.H., Keimel K., "Compact continuous L-domains", Comput. Math. Appl. 38(1) (1999), 81-89.
[8] Plotkin G.D., "A powerdomain construction", SIAM J. Comput. 5(3) (1976), 452-487.
Categories and General Algebraic Structures with Applications
Volume 8, Issue 1
January 2018
Pages 51-59

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