Compactly Completeness and Finitarily Completeness on Continuous Information System
DOI:
https://doi.org/10.24203/ajfam.v9i2.6577Keywords:
continuous information system , compactly completeness, finitarily completeness, posetAbstract
The plane here, introduce and study the concepts of bounded completeness and finitely completeness on continuous information system. Further more compactly completeness, finitarily completeness and strongly compactly completeness for continuous information system. Some interactions between these concepts are investigated. Some corresponding results in posets and domains due to R.Hechmann [5] are generalized.
References
S. Abramsky and A. Jung, domain theory in the Handbook for logic inComputer Science, Volume 3, Edited
by S. Abramsky, Dov M. Gabbay, and T. S. E. Maibaum, published by Clarendon Press, Oxford in 1994.
B. Branachewski and R. E. Hofmann (eds), Continuous lattices, Lecture Notes in Mathematices 871, SpringerVerlag, Berlin, Heidelberg, New York, 1981.
M. Erne, Scott convergence and Scott Topologies in Partially ordered sets II, in [BH] [2], pp. 61-96.
G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. s. Scott, A compendium of continuous
lattices, Springer Verlag, Berlin, Heidelberg, New York, 1980.
R. Heckmann, Power domain constuctions Ph. D. thesis, University Saarlandes, 1999.
( http://rwt.cs.unisb.de/heckman/diss/diss.html.)
R. E. Hofmann, Continuous Poset comletely distributive complete lattices and Hausdorff compactifications, in
, pp. 159-208.
R. E. Hofmann, Projective sober spaces, continuous lattices, Proc. Conf., Bremen 1979, Lect. Notes Math.,
(1981), pp. 125-158.
R. E. Hofmann, Sobrification of partially ordered sets, Semi-group Forum, Volume 17 (1979) 123-138.
R. Kummetz, Partially ordered sets with projections and their topology, pd. D. thesis; Dresden University of
Technology, 2000.
K. Larsen and G. Winskel, Using information systems to solve recursive domain equations effectively, in G.
Kahn, D. B. Mac-Queen and G. Plotkin, eds, Semantics of data types, Lecture Notes in Computer Science 173,
Springer -Veralg, Berlin,1984, 109-129.
J. D. Lawson, The duality of continuous posets, Houstan. J. Math., Volume5, No. 3(1979) 357-386.
J. D. Lawson, The Versatile continuous order, in Lecture Notes in Computer Science 298, Springer -Veralg,
Berlin, heidelberg, New Yourk, 1987, pp 134-160.
S. Lipschutz, Theory and problems of general topology, Schaum series, McJRAW-HILL INT., 1965.
G. Markowsky [1981a] , A motivation and generalization of Scott,
s notion of a continuous lattice, in [1979,
Bremen], in [BH] [2], pp. 298-307.
J. Nino-Salcedo, On continuous posets and their applications, Ph.D. thesis, Tulane University, 1981.
S. Vickers. Information systems for continuous posets, Theoretical Computer Science 114, SIssue 2 (1993)201-
P. Waszhiewicz, Quantitative continuous domain, Ph.D. thesis School of Computer Science, University of
Birmingham Edgbas-ton 2002.
Xinyang, FengJian Tang and Bijan DavvazYanfeng Luo, A novel study on fuzzy ideals and fuzzy filters of
ordered *-semigroups, Journal of Intelligent and Fuzzy Systems 33(1):423-431 · June 2017
Xiang-Yun Xie, Jian Tang and Bijan Davvaz, An investigation on hyper S-posets over ordered semihypergroups,
Open Mathematics 15(1) · February 2017
H. Zhang, Dualities of domains, Ph. D. thesis, Department of Mathematices, Tulane University, 1993.
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Mohammed M. Khalaf, Mohammed M. Ali Al-Shamiri
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.
