Clustering in Celebrating Professor Themba A. Dube (A TAD Celebration II)
This paper is the second in the series celebrating the mathematical works of Professor Themba Dube. In this sequel, we give prominence to Dube's pivotal contributions on pointfree convergence at the unstructured frame level, in the category of locales, and on his noteworthy conceptions on exten...
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Shahid Beheshti University
2025-01-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | https://cgasa.sbu.ac.ir/article_105284_0ab76d9706959aaf4eb2f621ef117cc9.pdf |
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| author | Inderasan Naidoo |
| author_facet | Inderasan Naidoo |
| author_sort | Inderasan Naidoo |
| collection | DOAJ |
| description | This paper is the second in the series celebrating the mathematical works of Professor Themba Dube. In this sequel, we give prominence to Dube's pivotal contributions on pointfree convergence at the unstructured frame level, in the category of locales, and on his noteworthy conceptions on extensions and frame quotients. We distill and draw attention to particular studies of Dube on filters and his novel characterizations of certain conservative pointfree properties by filter and ultrafilter convergence, notably normality, almost realcompactness, and pseudocompactness. We also feature Dube's joint work on convergence and clustering of filters in Loc and coconvergence and coclustering of ideals in the category Frm. |
| format | Article |
| id | doaj-art-632f0ef26b4941518453b732d03939fd |
| institution | Kabale University |
| issn | 2345-5853 2345-5861 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj-art-632f0ef26b4941518453b732d03939fd2025-01-24T18:43:40ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612025-01-0122154210.48308/cgasa.2025.105284105284Clustering in Celebrating Professor Themba A. Dube (A TAD Celebration II)Inderasan Naidoo0Department of Mathematical Sciences, University of South Africa, P.O.Box 392, Tshwane, UNISA 0003, South Africa. National Institute for Theoretical and Computational Sciences (NITheCS), Johannesburg, South Africa.This paper is the second in the series celebrating the mathematical works of Professor Themba Dube. In this sequel, we give prominence to Dube's pivotal contributions on pointfree convergence at the unstructured frame level, in the category of locales, and on his noteworthy conceptions on extensions and frame quotients. We distill and draw attention to particular studies of Dube on filters and his novel characterizations of certain conservative pointfree properties by filter and ultrafilter convergence, notably normality, almost realcompactness, and pseudocompactness. We also feature Dube's joint work on convergence and clustering of filters in Loc and coconvergence and coclustering of ideals in the category Frm.https://cgasa.sbu.ac.ir/article_105284_0ab76d9706959aaf4eb2f621ef117cc9.pdfframelocalekatˇetov extensionfomin extensionβlnormalpseudocompactalmost realcompactˇcech-completequotientfilterultrafilterclusteringconvergencecoconvergencecoclustering |
| spellingShingle | Inderasan Naidoo Clustering in Celebrating Professor Themba A. Dube (A TAD Celebration II) Categories and General Algebraic Structures with Applications frame locale katˇetov extension fomin extension βl normal pseudocompact almost realcompact ˇcech-complete quotient filter ultrafilter clustering convergence coconvergence coclustering |
| title | Clustering in Celebrating Professor Themba A. Dube (A TAD Celebration II) |
| title_full | Clustering in Celebrating Professor Themba A. Dube (A TAD Celebration II) |
| title_fullStr | Clustering in Celebrating Professor Themba A. Dube (A TAD Celebration II) |
| title_full_unstemmed | Clustering in Celebrating Professor Themba A. Dube (A TAD Celebration II) |
| title_short | Clustering in Celebrating Professor Themba A. Dube (A TAD Celebration II) |
| title_sort | clustering in celebrating professor themba a dube a tad celebration ii |
| topic | frame locale katˇetov extension fomin extension βl normal pseudocompact almost realcompact ˇcech-complete quotient filter ultrafilter clustering convergence coconvergence coclustering |
| url | https://cgasa.sbu.ac.ir/article_105284_0ab76d9706959aaf4eb2f621ef117cc9.pdf |
| work_keys_str_mv | AT inderasannaidoo clusteringincelebratingprofessorthembaadubeatadcelebrationii |