Mohammad Irshad KHODABOCUS, Noor-ul-hacq SOOKIA

4316

Theory of Generalized Sets in Generalized Topological Spaces

Several specific types of generalized sets (briefly, g-T_g-sets in generalized topological spaces (briefly, T_g-spaces have been defined and investigated for various purposes from time to time in the literature of T_g-spaces. Our recent research in the field of a new class of g-T_g-sets in T_g-spaces is reported herein as a starting point for more generalized classes. It is shown that the class of g-T_g-sets is a superclass of those whose elements are called open, closed, semi-open, semi-closed, pre-open, pre-closed, semi-pre-open, and semi-pre-closed sets in a T_g-space. A subclass of the T_g-subspace corresponds to the class of g-T_g-sets of a T_g-space. A class of g-T_g-sets of the Cartesian product of these T_g-spaces corresponds to the Cartesian product of a finite number of classes of g-T_g-sets, each of which belongs to a T_g-space. Diagrams establish the various relationships amongst the classes presented here and in the literature, and an ad hoc application supports the overall theory.
Keywords:

Generalized topology, Generalized topological space, Generalized operations Generalized open sets, Generalized closed sets,

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Journal of New Theory-Cover
  • Yayın Aralığı: Yılda 4 Sayı
  • Başlangıç: 2014
  • Yayıncı: Naim Çağman
Arşiv
Sayıdaki Diğer Makaleler

Manuel FERNANDEZ-GUASTİ

Monalisa MİDDYA

Hasan BULUT

Mohammad Irshad KHODABOCUS, Noor-ul-hacq SOOKIA