On relatively connected sublocales and J-frames
In this paper, we present a study of relatively connected sublocales. Connected sublocales are relatively connected, not conversely. We study conditions under which relatively connected sublocales are connected. The development of this study is subsequently utilized to characterize what we call C-no...
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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_104809_c4177eaa5a9132ce323afa47e567ed42.pdf |
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| _version_ | 1832586952265695232 |
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| author | Simo Mthethwa Siyabonga Dubazana |
| author_facet | Simo Mthethwa Siyabonga Dubazana |
| author_sort | Simo Mthethwa |
| collection | DOAJ |
| description | In this paper, we present a study of relatively connected sublocales. Connected sublocales are relatively connected, not conversely. We study conditions under which relatively connected sublocales are connected. The development of this study is subsequently utilized to characterize what we call C-normal frames. We show that normal frames are C-normal but not conversely. Some results concerning J-frames are presented; amongst other things, we prove that regular continuous frames are rim-compact. A rim-compact J-frame is regular continuous. The latter is used to show that the least compactification of a regular continuous J-frame coincides with its Freudenthal compactification. In turn, this contributes to the known conditions under which the least compactification is perfect. |
| format | Article |
| id | doaj-art-adc2b6af7e254809af35408a10fac43d |
| 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-adc2b6af7e254809af35408a10fac43d2025-01-24T18:43:40ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612025-01-0122118119610.48308/cgasa.2024.235270.1481104809On relatively connected sublocales and J-framesSimo Mthethwa0Siyabonga Dubazana1School of Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa.School of Mathematics, Statistics and Computer Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa.In this paper, we present a study of relatively connected sublocales. Connected sublocales are relatively connected, not conversely. We study conditions under which relatively connected sublocales are connected. The development of this study is subsequently utilized to characterize what we call C-normal frames. We show that normal frames are C-normal but not conversely. Some results concerning J-frames are presented; amongst other things, we prove that regular continuous frames are rim-compact. A rim-compact J-frame is regular continuous. The latter is used to show that the least compactification of a regular continuous J-frame coincides with its Freudenthal compactification. In turn, this contributes to the known conditions under which the least compactification is perfect.https://cgasa.sbu.ac.ir/article_104809_c4177eaa5a9132ce323afa47e567ed42.pdfj-framesrelatively connected sublocalesc-normalfreudenthalcontinuous framesperfect compactificationrim-compact |
| spellingShingle | Simo Mthethwa Siyabonga Dubazana On relatively connected sublocales and J-frames Categories and General Algebraic Structures with Applications j-frames relatively connected sublocales c-normal freudenthal continuous frames perfect compactification rim-compact |
| title | On relatively connected sublocales and J-frames |
| title_full | On relatively connected sublocales and J-frames |
| title_fullStr | On relatively connected sublocales and J-frames |
| title_full_unstemmed | On relatively connected sublocales and J-frames |
| title_short | On relatively connected sublocales and J-frames |
| title_sort | on relatively connected sublocales and j frames |
| topic | j-frames relatively connected sublocales c-normal freudenthal continuous frames perfect compactification rim-compact |
| url | https://cgasa.sbu.ac.ir/article_104809_c4177eaa5a9132ce323afa47e567ed42.pdf |
| work_keys_str_mv | AT simomthethwa onrelativelyconnectedsublocalesandjframes AT siyabongadubazana onrelativelyconnectedsublocalesandjframes |