Version 1
: Received: 17 April 2024 / Approved: 17 April 2024 / Online: 17 April 2024 (09:00:22 CEST)
How to cite:
Taha, I.M. On Double Fuzzy Topological Spaces: Some New Types of Separation Axioms, Continuity, and Compactness. Preprints2024, 2024041125. https://doi.org/10.20944/preprints202404.1125.v1
Taha, I.M. On Double Fuzzy Topological Spaces: Some New Types of Separation Axioms, Continuity, and Compactness. Preprints 2024, 2024041125. https://doi.org/10.20944/preprints202404.1125.v1
Taha, I.M. On Double Fuzzy Topological Spaces: Some New Types of Separation Axioms, Continuity, and Compactness. Preprints2024, 2024041125. https://doi.org/10.20944/preprints202404.1125.v1
APA Style
Taha, I.M. (2024). On Double Fuzzy Topological Spaces: Some New Types of Separation Axioms, Continuity, and Compactness. Preprints. https://doi.org/10.20944/preprints202404.1125.v1
Chicago/Turabian Style
Taha, I.M. 2024 "On Double Fuzzy Topological Spaces: Some New Types of Separation Axioms, Continuity, and Compactness" Preprints. https://doi.org/10.20944/preprints202404.1125.v1
Abstract
In this article, we first introduced new types of higher separation axioms called (r,s)-GFS-regular and (r,s)-GFS-normal spaces with the help of (r,s)-generalized fuzzy semi-closed sets (briefly, (r,s)-gfsc sets) and discussed some topological properties of them. Thereafter, we defined a stronger form of (r,s)-gfsc sets called (r,s)-g*fsc sets and investigated some of its features. Moreover, we showed that (r,s)-fsc set → (r,s)-g*fsc set → (r,s)-gfsc set, but the converse may not be true. In addition, we explored new types of fuzzy generalized mappings between double fuzzy topological spaces (U, τ, τ*) and (V, η, η*), and the relationships between these classes of mappings were examined with the help of some illustrative examples. Finally, some new types of compactness via (r,s)-gfso sets were defined and the relationships between them were introduced.
Computer Science and Mathematics, Geometry and Topology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
