Abstract
In this paper, initial and product graded ditopologies are formulated and accordingly it is shown that $\mathbf{dfGDitop}$ is topological over $\mathbf{dfTex}\times\mathbf{dfTex}$. By means of spectrum idea, (di)compactness in graded ditological texture spaces is defined as a generalization of (di)compactness in ditopological case and its relation with the ditopological case is investigated. Moreover, using graded difilters, two characterizations of dicompactness of graded ditological texture spaces are obtained.
Highlights
The idea “graded ditopology” has been introduced in [7] by Brown and Šostak
Initial and product graded ditopologies are formulated and it is shown that dfGDitop is a topological structure over dfTex dfTex
By means of spectrum idea,compactness in graded ditological texture spaces is defined as a generalization ofcompactness in ditopological case and its relation with the ditopological case is investigated
Summary
The idea “graded ditopology” has been introduced in [7] by Brown and Šostak. This new structure is more comprehensive than ditopologies basically given in [2, 3] and fuzzy topologies given independently by Šostak in [11] and Kubiak in [10]. Graded Ditopological Texture Spaces: [7] Let (S; S ), (V; V ) be textures and consider T ; K : S ! T is called a (V; V )-graded topology, K a (V; V )-graded cotopology and (T ; K ) a (V; V )-graded ditopology on (S; S ) and for any graded ditopological texture space (S; S ; T ; K ;V; V ) and for each v 2 V it is defined that. [7] Let (Sk; Sk; Tk; Kk;Vk; Vk), k = 1; 2 be graded ditopological texture spaces, ( f ; F) : (S1; S1) ! [7] The class of graded ditopological texture spaces and relatively bicontinuous difunction pairs between them form a category denoted by dfGDitop Theorem 1.15. [7] The class of graded ditopological texture spaces and relatively bicontinuous difunction pairs between them form a category denoted by dfGDitop
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
