Objects generated by an arbitrary natural number. Part 4: New aspects

Krassimir Atanassov
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 3, Pages 589–597
DOI: 10.7546/nntdm.2023.29.3.589-597
Full paper (PDF, 229 Kb)

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Authors and affiliations

Krassimir Atanassov
¹   Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
“Acad. G. Bonchev” Str., Bl. 105, Sofia-1113, Bulgaria
²   Intelligent Systems Laboratory, “Prof. Dr Asen Zlatarov” University
1 “Prof. Yakimov” Blvd., Burgas-8000, Bulgaria

Abstract

The set , generated by an arbitrary natural number , was defined in [3]. There, and in [5,6], some arithmetic functions and arithmetic operators of a modal and topological types are defined over the elements of . Here, over the elements of new arithmetic functions are defined and some of their basic properties are studied. Two standard modal topological structures over are described. Perspectives for future research are discussed.

Keywords

• Arithmetic function
• Modal operator
• Natural number
• Set
• Topological operator

2020 Mathematics Subject Classification

• 11A25

References

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3. Atanassov, K. (2020). Objects generated by an arbitrary natural number. Notes on Number Theory and Discrete Mathematics, 26(4), 57–62.
4. Atanassov, K. (2022). Intuitionistic fuzzy modal topological structure. Mathematics, 10(18), Article ID 3313.
5. Atanassov, K. (2022). Objects generated by an arbitrary natural number. Part 2: Modal aspect. Notes on Number Theory and Discrete Mathematics, 28(3), 558–563.
6. Atanassov, K. (2023). Objects generated by an arbitrary natural number. Part 3: Standard modal-topological aspect. Notes on Number Theory and Discrete Mathematics, 29(1), 171–180.
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14. Sternberg, S. (1964). Lectures on Differential Geometry. Prentice Hall, Englewood, NJ.

Manuscript history

• Received: 8 February 2023
• Revised: 26 July 2023
• Accepted: 19 August 2023
• Online First: 25 August 2023

Copyright information

Ⓒ 2023 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).