On Semitopological De Morgan Residuated Lattices
عنوان مقاله: On Semitopological De Morgan Residuated Lattices
شناسه ملی مقاله: JR_TFSS-2-1_008
منتشر شده در در سال 1402
شناسه ملی مقاله: JR_TFSS-2-1_008
منتشر شده در در سال 1402
مشخصات نویسندگان مقاله:
Liviu-Constantin Holdon - Die Fakultt fr Unternehmertum, Ingenieurwissenschaften und Geschftsfhrung Ingenieurwissenschaften und Management Polytechnische Universitt Bukarest, Splaiul Independentei st., RO-۰۶۰۰۴۲ Bucharest (۶), Romania E-mail: holdon_liviu@yahoo.com Internatio
خلاصه مقاله:
Liviu-Constantin Holdon - Die Fakultt fr Unternehmertum, Ingenieurwissenschaften und Geschftsfhrung Ingenieurwissenschaften und Management Polytechnische Universitt Bukarest, Splaiul Independentei st., RO-۰۶۰۰۴۲ Bucharest (۶), Romania E-mail: holdon_liviu@yahoo.com Internatio
The class of De Morgan residuated lattices was introduced by L. C. Holdon (Kybernetika ۵۴(۳):۴۴۳-۴۷۵, ۲۰۱۸), recently, many mathematicians have studied the theory of ideals or filters in De Morgan residuated lattices and some of them investigated the properties of De Morgan residuated lattices endowed with a topology. In this paper, we introduce the notion of semitopological De Morgan residuated lattice, we present some examples and by considering the notion of upsets, for any element a of a De Morgan residuated lattice L, there is a topology \tau_{a} on L and we show that L endowed with the topology \tau_{a} is semitopological with respect to \vee, \wedge and \odot, and right topological with respect to \rightarrow. Moreover, in the general case of residuated lattices we prove that L endowed with the topology \tau_{a} is semitopological with respect to \odot and right topological with respect to \rightarrow. Finally, we obtain some of the topological aspects of this structure such as L endowed with the topology \tau_{a} is a \mathbf{T_۰}-space, but it is not a \mathbf{T_۱}-space or Hausdorff space.
کلمات کلیدی: Residuated lattice, De Morgan laws, De Morgan residuated lattice, Filter, Semitopological algebras, Hausdorff space
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1662379/