Тhe concept of topological well-ordered space
UDC 515.12 Since the general definition of topology is based on the characteristics of the standard Euclidean topology, the relationships between the ordering on real numbers and its topology have been generalized over time and studied in numerous aspects. The compatibility of partially...
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| Datum: | 2023 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7145 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512611828760576 |
|---|---|
| author | Kandemir, Mustafa Burç Uludağ, Dilan Başak Kandemir, Mustafa Burç Uludağ, Dilan Başak |
| author_facet | Kandemir, Mustafa Burç Uludağ, Dilan Başak Kandemir, Mustafa Burç Uludağ, Dilan Başak |
| author_sort | Kandemir, Mustafa Burç |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-07-02T07:08:16Z |
| description | UDC 515.12
Since the general definition of topology is based on the characteristics of the standard Euclidean topology, the relationships between the ordering on real numbers and its topology have been generalized over time and studied in numerous aspects. The compatibility of partially ordered sets with the topology on them was  studied by many researchers.  On the other hand, well-orderedness is an important concept of the set theory.  We define the concept of topological well-orderedness, which can be regarded as a topological generalization of well-orderedness in the set theory, and analyze its basic properties.  In this way, the relationship between well-orderedness and topology is  established from a different point of view.  Finally, some basic applications of the concept of topological  well-orderedness to the graph theory are investigated. |
| doi_str_mv | 10.37863/umzh.v75i6.7145 |
| first_indexed | 2026-03-24T03:31:33Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7145 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:31:33Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-71452023-07-02T07:08:16Z Тhe concept of topological well-ordered space Тhe concept of topological well-ordered space Kandemir, Mustafa Burç Uludağ, Dilan Başak Kandemir, Mustafa Burç Uludağ, Dilan Başak Poset Topology Well-ordered set Topological well-ordered space Graph theory UDC 515.12 Since the general definition of topology is based on the characteristics of the standard Euclidean topology, the relationships between the ordering on real numbers and its topology have been generalized over time and studied in numerous aspects. The compatibility of partially ordered sets with the topology on them was  studied by many researchers.  On the other hand, well-orderedness is an important concept of the set theory.  We define the concept of topological well-orderedness, which can be regarded as a topological generalization of well-orderedness in the set theory, and analyze its basic properties.  In this way, the relationship between well-orderedness and topology is  established from a different point of view.  Finally, some basic applications of the concept of topological  well-orderedness to the graph theory are investigated. УДК 515.12 Поняття топологічного добре впорядкованого простору Оскільки загальне визначення топології ґрунтується на характеристиках стандартної евклідової топології, зв’язки між упорядкуванням дійсних чисел та відповідною топологією були з часом  узагальнені та вивчені з багатьох точок зору. Сумісність частково впорядкованих множин з топологією на них вивчалась багатьма дослідниками. З іншого боку, строга впорядкованість є важливим поняттям теорії множин. Визначено поняття топологічної впорядкованості, яку можна розглядати як топологічне узагальнення поняття строгої впорядкованості в теорії множин, та досліджено її основні властивості. Таким чином, зв'язок між строгою впорядкованістю і топологією був встановлений з іншої точки зору.  Крім того, досліджено деякі основні застосування поняття топологічної впорядкованості до теорії графів. Institute of Mathematics, NAS of Ukraine 2023-06-20 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7145 10.37863/umzh.v75i6.7145 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 6 (2023); 817 - 829 Український математичний журнал; Том 75 № 6 (2023); 817 - 829 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7145/9765 Copyright (c) 2023 Mustafa Burç Kandemir |
| spellingShingle | Kandemir, Mustafa Burç Uludağ, Dilan Başak Kandemir, Mustafa Burç Uludağ, Dilan Başak Тhe concept of topological well-ordered space |
| title | Тhe concept of topological well-ordered space |
| title_alt | Тhe concept of topological well-ordered space |
| title_full | Тhe concept of topological well-ordered space |
| title_fullStr | Тhe concept of topological well-ordered space |
| title_full_unstemmed | Тhe concept of topological well-ordered space |
| title_short | Тhe concept of topological well-ordered space |
| title_sort | тhe concept of topological well-ordered space |
| topic_facet | Poset Topology Well-ordered set Topological well-ordered space Graph theory |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7145 |
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