Soft Connectedness, Soft Path Connectedness and the Category of Soft Topological Groups Article Swipe
In this study, the soft usual topology compatible with the usual topology of $\mathbb{R}$ is defined, and using its subspace topology on the interval $[0,1]$, the concept of a soft path is introduced. Within this context, the notions of soft connectedness and soft path connectedness are developed, their relationship is analyzed, and it is shown that these properties are preserved under soft continuous mappings. Moreover, the behavior of these concepts within soft topological groups is investigated in detail. Finally, the category of soft topological groups is constructed, its morphisms are identified, and it is shown that this category forms a symmetric monoidal category.
Related Topics
Concepts
Metadata
- Type
- article
- Landing Page
- http://arxiv.org/abs/2511.12724
- https://arxiv.org/pdf/2511.12724
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7106094290
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W7106094290Canonical identifier for this work in OpenAlex
- Title
-
Soft Connectedness, Soft Path Connectedness and the Category of Soft Topological GroupsWork title
- Type
-
articleOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
-
2025-11-16Full publication date if available
- Authors
-
Alemdar, Nazmiye, Akız, Hürmet Fulya, Ayaz, HalimList of authors in order
- Landing page
-
https://arxiv.org/abs/2511.12724Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2511.12724Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2511.12724Direct OA link when available
- Concepts
-
Social connectedness, Mathematics, Topology (electrical circuits), Topological space, Path (computing), Subspace topology, Category of topological spaces, Morphism, Algebraic topology, General topology, Soft set, Group (periodic table), Network topology, Pure mathematicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
Full payload
| id | https://openalex.org/W7106094290 |
|---|---|
| doi | |
| ids.openalex | https://openalex.org/W7106094290 |
| fwci | 0.0 |
| type | article |
| title | Soft Connectedness, Soft Path Connectedness and the Category of Soft Topological Groups |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T11671 |
| topics[0].field.id | https://openalex.org/fields/18 |
| topics[0].field.display_name | Decision Sciences |
| topics[0].score | 0.9904394149780273 |
| topics[0].domain.id | https://openalex.org/domains/2 |
| topics[0].domain.display_name | Social Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1803 |
| topics[0].subfield.display_name | Management Science and Operations Research |
| topics[0].display_name | Fuzzy and Soft Set Theory |
| topics[1].id | https://openalex.org/T12923 |
| topics[1].field.id | https://openalex.org/fields/17 |
| topics[1].field.display_name | Computer Science |
| topics[1].score | 0.004046858288347721 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/1707 |
| topics[1].subfield.display_name | Computer Vision and Pattern Recognition |
| topics[1].display_name | Digital Image Processing Techniques |
| topics[2].id | https://openalex.org/T11151 |
| topics[2].field.id | https://openalex.org/fields/26 |
| topics[2].field.display_name | Mathematics |
| topics[2].score | 0.0008660331950522959 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2608 |
| topics[2].subfield.display_name | Geometry and Topology |
| topics[2].display_name | Advanced Topology and Set Theory |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C201943243 |
| concepts[0].level | 2 |
| concepts[0].score | 0.7636333703994751 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q7551008 |
| concepts[0].display_name | Social connectedness |
| concepts[1].id | https://openalex.org/C33923547 |
| concepts[1].level | 0 |
| concepts[1].score | 0.6774061322212219 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[1].display_name | Mathematics |
| concepts[2].id | https://openalex.org/C184720557 |
| concepts[2].level | 2 |
| concepts[2].score | 0.6224616169929504 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q7825049 |
| concepts[2].display_name | Topology (electrical circuits) |
| concepts[3].id | https://openalex.org/C81332173 |
| concepts[3].level | 2 |
| concepts[3].score | 0.5433884263038635 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q179899 |
| concepts[3].display_name | Topological space |
| concepts[4].id | https://openalex.org/C2777735758 |
| concepts[4].level | 2 |
| concepts[4].score | 0.5176261067390442 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q817765 |
| concepts[4].display_name | Path (computing) |
| concepts[5].id | https://openalex.org/C32834561 |
| concepts[5].level | 2 |
| concepts[5].score | 0.4809283912181854 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q660730 |
| concepts[5].display_name | Subspace topology |
| concepts[6].id | https://openalex.org/C83177873 |
| concepts[6].level | 5 |
| concepts[6].score | 0.44880130887031555 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q2000555 |
| concepts[6].display_name | Category of topological spaces |
| concepts[7].id | https://openalex.org/C137212723 |
| concepts[7].level | 2 |
| concepts[7].score | 0.36847540736198425 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q1948412 |
| concepts[7].display_name | Morphism |
| concepts[8].id | https://openalex.org/C145054310 |
| concepts[8].level | 3 |
| concepts[8].score | 0.3297649025917053 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q212803 |
| concepts[8].display_name | Algebraic topology |
| concepts[9].id | https://openalex.org/C129089157 |
| concepts[9].level | 3 |
| concepts[9].score | 0.314662903547287 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q621550 |
| concepts[9].display_name | General topology |
| concepts[10].id | https://openalex.org/C2777037408 |
| concepts[10].level | 3 |
| concepts[10].score | 0.2942676544189453 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q4310193 |
| concepts[10].display_name | Soft set |
| concepts[11].id | https://openalex.org/C2781311116 |
| concepts[11].level | 2 |
| concepts[11].score | 0.2880249321460724 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q83306 |
| concepts[11].display_name | Group (periodic table) |
| concepts[12].id | https://openalex.org/C199845137 |
| concepts[12].level | 2 |
| concepts[12].score | 0.28404566645622253 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q145490 |
| concepts[12].display_name | Network topology |
| concepts[13].id | https://openalex.org/C202444582 |
| concepts[13].level | 1 |
| concepts[13].score | 0.2614573836326599 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q837863 |
| concepts[13].display_name | Pure mathematics |
| keywords[0].id | https://openalex.org/keywords/social-connectedness |
| keywords[0].score | 0.7636333703994751 |
| keywords[0].display_name | Social connectedness |
| keywords[1].id | https://openalex.org/keywords/topology |
| keywords[1].score | 0.6224616169929504 |
| keywords[1].display_name | Topology (electrical circuits) |
| keywords[2].id | https://openalex.org/keywords/topological-space |
| keywords[2].score | 0.5433884263038635 |
| keywords[2].display_name | Topological space |
| keywords[3].id | https://openalex.org/keywords/path |
| keywords[3].score | 0.5176261067390442 |
| keywords[3].display_name | Path (computing) |
| keywords[4].id | https://openalex.org/keywords/subspace-topology |
| keywords[4].score | 0.4809283912181854 |
| keywords[4].display_name | Subspace topology |
| keywords[5].id | https://openalex.org/keywords/category-of-topological-spaces |
| keywords[5].score | 0.44880130887031555 |
| keywords[5].display_name | Category of topological spaces |
| language | |
| locations[0].id | pmh:oai:arXiv.org:2511.12724 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400194 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | arXiv (Cornell University) |
| locations[0].source.host_organization | https://openalex.org/I205783295 |
| locations[0].source.host_organization_name | Cornell University |
| locations[0].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[0].license | |
| locations[0].pdf_url | https://arxiv.org/pdf/2511.12724 |
| locations[0].version | submittedVersion |
| locations[0].raw_type | text |
| locations[0].license_id | |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | |
| locations[0].landing_page_url | http://arxiv.org/abs/2511.12724 |
| indexed_in | arxiv |
| authorships[0].author.id | |
| authorships[0].author.orcid | |
| authorships[0].author.display_name | Alemdar, Nazmiye |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Alemdar, Nazmiye |
| authorships[0].is_corresponding | True |
| authorships[1].author.id | |
| authorships[1].author.orcid | |
| authorships[1].author.display_name | Akız, Hürmet Fulya |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Akız, Hürmet Fulya |
| authorships[1].is_corresponding | False |
| authorships[2].author.id | |
| authorships[2].author.orcid | |
| authorships[2].author.display_name | Ayaz, Halim |
| authorships[2].author_position | last |
| authorships[2].raw_author_name | Ayaz, Halim |
| authorships[2].is_corresponding | False |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/2511.12724 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-11-19T00:00:00 |
| display_name | Soft Connectedness, Soft Path Connectedness and the Category of Soft Topological Groups |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-19T23:39:43.309859 |
| primary_topic.id | https://openalex.org/T11671 |
| primary_topic.field.id | https://openalex.org/fields/18 |
| primary_topic.field.display_name | Decision Sciences |
| primary_topic.score | 0.9904394149780273 |
| primary_topic.domain.id | https://openalex.org/domains/2 |
| primary_topic.domain.display_name | Social Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1803 |
| primary_topic.subfield.display_name | Management Science and Operations Research |
| primary_topic.display_name | Fuzzy and Soft Set Theory |
| cited_by_count | 0 |
| locations_count | 1 |
| best_oa_location.id | pmh:oai:arXiv.org:2511.12724 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | |
| best_oa_location.pdf_url | https://arxiv.org/pdf/2511.12724 |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | text |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | http://arxiv.org/abs/2511.12724 |
| primary_location.id | pmh:oai:arXiv.org:2511.12724 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | https://arxiv.org/pdf/2511.12724 |
| primary_location.version | submittedVersion |
| primary_location.raw_type | text |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | http://arxiv.org/abs/2511.12724 |
| publication_date | 2025-11-16 |
| publication_year | 2025 |
| referenced_works_count | 0 |
| abstract_inverted_index.a | 28, 99 |
| abstract_inverted_index.In | 0 |
| abstract_inverted_index.in | 76 |
| abstract_inverted_index.is | 14, 31, 49, 53, 74, 85, 93 |
| abstract_inverted_index.it | 52, 92 |
| abstract_inverted_index.of | 12, 27, 38, 67, 81 |
| abstract_inverted_index.on | 21 |
| abstract_inverted_index.and | 16, 41, 51, 91 |
| abstract_inverted_index.are | 45, 58, 89 |
| abstract_inverted_index.its | 18, 87 |
| abstract_inverted_index.the | 3, 9, 22, 25, 36, 65, 79 |
| abstract_inverted_index.path | 30, 43 |
| abstract_inverted_index.soft | 4, 29, 39, 42, 61, 71, 82 |
| abstract_inverted_index.that | 55, 95 |
| abstract_inverted_index.this | 1, 34, 96 |
| abstract_inverted_index.with | 8 |
| abstract_inverted_index.forms | 98 |
| abstract_inverted_index.shown | 54, 94 |
| abstract_inverted_index.their | 47 |
| abstract_inverted_index.these | 56, 68 |
| abstract_inverted_index.under | 60 |
| abstract_inverted_index.using | 17 |
| abstract_inverted_index.usual | 5, 10 |
| abstract_inverted_index.Within | 33 |
| abstract_inverted_index.groups | 73, 84 |
| abstract_inverted_index.study, | 2 |
| abstract_inverted_index.within | 70 |
| abstract_inverted_index.concept | 26 |
| abstract_inverted_index.detail. | 77 |
| abstract_inverted_index.notions | 37 |
| abstract_inverted_index.$[0,1]$, | 24 |
| abstract_inverted_index.Finally, | 78 |
| abstract_inverted_index.behavior | 66 |
| abstract_inverted_index.category | 80, 97 |
| abstract_inverted_index.concepts | 69 |
| abstract_inverted_index.context, | 35 |
| abstract_inverted_index.defined, | 15 |
| abstract_inverted_index.interval | 23 |
| abstract_inverted_index.monoidal | 101 |
| abstract_inverted_index.subspace | 19 |
| abstract_inverted_index.topology | 6, 11, 20 |
| abstract_inverted_index.Moreover, | 64 |
| abstract_inverted_index.analyzed, | 50 |
| abstract_inverted_index.category. | 102 |
| abstract_inverted_index.mappings. | 63 |
| abstract_inverted_index.morphisms | 88 |
| abstract_inverted_index.preserved | 59 |
| abstract_inverted_index.symmetric | 100 |
| abstract_inverted_index.compatible | 7 |
| abstract_inverted_index.continuous | 62 |
| abstract_inverted_index.developed, | 46 |
| abstract_inverted_index.properties | 57 |
| abstract_inverted_index.identified, | 90 |
| abstract_inverted_index.introduced. | 32 |
| abstract_inverted_index.topological | 72, 83 |
| abstract_inverted_index.$\mathbb{R}$ | 13 |
| abstract_inverted_index.constructed, | 86 |
| abstract_inverted_index.investigated | 75 |
| abstract_inverted_index.relationship | 48 |
| abstract_inverted_index.connectedness | 40, 44 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.86975634 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |