Branch Mathematics and Statistics Faculty and Staff Publications
Document Type
Book
Publication Date
2023
Abstract
In general, a system S (that may be a company, association, institution, society, country, etc.) is formed by sub-systems Si { or P(S), the powerset of S }, and each sub-system Si is formed by sub-sub-systems Sij { or P(P(S)) = P^2(S) } and so on.
That’s why the n-th PowerSet of a Set S { defined recursively and denoted by P^n(S) = P(P^(n-1)(S) } was introduced, to better describes the organization of people, beings, objects etc. in our real world.
The n-th PowerSet was used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra.
In general, in any field of knowledge, one in fact encounters SuperHyperStructures, https://fs.unm.edu/SuperHyperAlgebra.pdf.
Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology, http://fs.unm.edu/TT/.
Language (ISO)
English
Keywords
n-th PowerSet, System, Sub-System, Sub-Sub-Syatem, SuperHyperOperation, SuperHyperAxiom, Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom, SuperHyperAlgebra, Neutrosophic SuperHyperAlgebra, SuperHyperStructure, Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, Neutrosophic SuperHyperTopology
Recommended Citation
Smarandache, Florentin; Memet Sahin; Derya Bakbak; Vakkas Uluçay; and Abdullah Kargı. "Neutrosophic SuperHyperAlgebra And New Types of Topologies." (2023). https://digitalrepository.unm.edu/math_fsp/605
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
