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Furstenberg topology and Collatz problem
Journal
Axioms
20
Author
Tutaj Edward
Tutaj-Gasińska Halszka
Volume
14
Number
4
Article ID
297
ISSN
2075-1680
Keywords in English
Collatz conjecture
arithmetic sequence
Furstenberg topology
stopping time
Access date
2025-05-09
Language
English
Journal language
English
Abstract in English
The aims of this paper are two-fold. First, we present the result of the decomposition on the iterations of a Collatz transform into arithmetic sequences. With this, we prove that in Furstenberg topology, the set of (odd) integers with an infinite stopping time is closed and nowhere dense. Then, we move our considerations to some monoids 𝕃 in ℕ, where we define a suitably modified Collatz transform, and we present some results of numerical investigations on the behaviour of these modified transforms.
Affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki
| dc.abstract.en | The aims of this paper are two-fold. First, we present the result of the decomposition on the iterations of a Collatz transform into arithmetic sequences. With this, we prove that in Furstenberg topology, the set of (odd) integers with an infinite stopping time is closed and nowhere dense. Then, we move our considerations to some monoids 𝕃 in ℕ, where we define a suitably modified Collatz transform, and we present some results of numerical investigations on the behaviour of these modified transforms. | |
| dc.affiliation | Wydział Matematyki i Informatyki : Instytut Matematyki | |
| dc.contributor.author | Tutaj, Edward - 132454 | |
| dc.contributor.author | Tutaj-Gasińska, Halszka - 132455 | |
| dc.date.accession | 2025-05-09 | |
| dc.date.accessioned | 2025-05-09T09:48:47Z | |
| dc.date.available | 2025-05-09T09:48:47Z | |
| dc.date.createdat | 2025-04-17T09:22:52Z | en |
| dc.date.issued | 2025 | |
| dc.date.openaccess | 0 | |
| dc.description.accesstime | w momencie opublikowania | |
| dc.description.number | 4 | |
| dc.description.version | ostateczna wersja wydawcy | |
| dc.description.volume | 14 | |
| dc.identifier.articleid | 297 | |
| dc.identifier.doi | 10.3390/axioms14040297 | |
| dc.identifier.issn | 2075-1680 | |
| dc.identifier.uri | https://ruj.uj.edu.pl/handle/item/552183 | |
| dc.identifier.weblink | https://www.mdpi.com/2075-1680/14/4/297 | |
| dc.language | eng | |
| dc.language.container | eng | |
| dc.rights | Dodaję tylko opis bibliograficzny | |
| dc.rights.licence | CC-BY | |
| dc.share.type | otwarte czasopismo | |
| dc.subject.en | Collatz conjecture | |
| dc.subject.en | arithmetic sequence | |
| dc.subject.en | Furstenberg topology | |
| dc.subject.en | stopping time | |
| dc.subtype | Article | |
| dc.title | Furstenberg topology and Collatz problem | |
| dc.title.journal | Axioms | |
| dc.type | JournalArticle | |
| dspace.entity.type | Publication | en |
dc.abstract.en
The aims of this paper are two-fold. First, we present the result of the decomposition on the iterations of a Collatz transform into arithmetic sequences. With this, we prove that in Furstenberg topology, the set of (odd) integers with an infinite stopping time is closed and nowhere dense. Then, we move our considerations to some monoids 𝕃 in ℕ, where we define a suitably modified Collatz transform, and we present some results of numerical investigations on the behaviour of these modified transforms. dc.affiliation
Wydział Matematyki i Informatyki : Instytut Matematyki dc.contributor.author
Tutaj, Edward - 132454 dc.contributor.author
Tutaj-Gasińska, Halszka - 132455 dc.date.accession
2025-05-09 dc.date.accessioned
2025-05-09T09:48:47Z dc.date.available
2025-05-09T09:48:47Z dc.date.createdaten
2025-04-17T09:22:52Z dc.date.issued
2025 dc.date.openaccess
0 dc.description.accesstime
w momencie opublikowania dc.description.number
4 dc.description.version
ostateczna wersja wydawcy dc.description.volume
14 dc.identifier.articleid
297 dc.identifier.doi
10.3390/axioms14040297 dc.identifier.issn
2075-1680 dc.identifier.uri
https://ruj.uj.edu.pl/handle/item/552183 dc.identifier.weblink
https://www.mdpi.com/2075-1680/14/4/297 dc.language
eng dc.language.container
eng dc.rights
Dodaję tylko opis bibliograficzny dc.rights.licence
CC-BY dc.share.type
otwarte czasopismo dc.subject.en
Collatz conjecture dc.subject.en
arithmetic sequence dc.subject.en
Furstenberg topology dc.subject.en
stopping time dc.subtype
Article dc.title
Furstenberg topology and Collatz problem dc.title.journal
Axioms dc.type
JournalArticle dspace.entity.typeen
Publication Affiliations
Wydział Matematyki i Informatyki
Tutaj, Edward
mathematics
Tutaj-Gasińska, Halszka
mathematics
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