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Lattice Operators and Topologies
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-01-13
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
Working within a complete (not necessarily atomic) Boolean algebra, we use a sublattice to define a topology on that algebra.
Our operators generalize complement on a lattice which in turn abstracts the set theoretic operator.
Less restricted than those of Banaschewski and Samuel, the operators exhibit some surprising behaviors.
We consider properties of such lattices and their interrelations.
Many of these properties are abstractions and generalizations of topological spaces.
The approach is similar to that of Bachman and Cohen.
It is in the spirit of Alexandroff, Frolík, and Nöbeling, although the setting is more general.
Proceeding in this manner, we can handle diverse topological theorems systematically before specializing to get as corollaries as the topological results of Alexandroff, Alo and Shapiro, Dykes, Frolík, and Ramsay.
American Psychological Association (APA)
Cogan, Eva. 2010. Lattice Operators and Topologies. International Journal of Mathematics and Mathematical Sciences،Vol. 2009, no. 2009, pp.1-13.
https://search.emarefa.net/detail/BIM-474425
Modern Language Association (MLA)
Cogan, Eva. Lattice Operators and Topologies. International Journal of Mathematics and Mathematical Sciences No. 2009 (2009), pp.1-13.
https://search.emarefa.net/detail/BIM-474425
American Medical Association (AMA)
Cogan, Eva. Lattice Operators and Topologies. International Journal of Mathematics and Mathematical Sciences. 2010. Vol. 2009, no. 2009, pp.1-13.
https://search.emarefa.net/detail/BIM-474425
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-474425